PSPL Model Classes

PSPL

class model.PSPL_PhotAstrom_noPar_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_noParallax, PSPL_PhotAstromParam1

PSPL model for astrometry and photometry - physical parameterization.

A Point Source Point Lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens mass and positions and proper motions of both the lens and source.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

mL: float

Mass of the lens (Msun)

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

beta: float

Angular distance between the lens and source on the plane of the sky (mas). Can be

• positive (u0_amp > 0 when u0_hat[0] < 0) or

• negative (u0_amp < 0 when u0_hat[0] > 0).

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

Ratio of Distance from the obersver to the lens to Distance from the observer to the source

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t)	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Not supported on this object.

get_amplification(t)

Get an array of the photometric amplifications at the input times. No parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. No parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Parallax

class model.PSPL_PhotAstrom_Par_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax, PSPL_PhotAstromParam1

PSPL model for astrometry and photometry - physical parameterization.

A Point Source Point Lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens mass and positions and proper motions of both the lens and source.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

mL: float

Mass of the lens (Msun)

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

beta: float

Angular distance between the lens and source on the plane of the sky (mas). Can be

• positive (u0_amp > 0 when u0_hat[0] < 0) or

• negative (u0_amp < 0 when u0_hat[0] > 0).

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

Ratio of Distance from the obersver to the lens to Distance from the observer to the source

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_LumLens_Par_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax_LumLens, PSPL_PhotAstromParam1

PSPL model for astrometry and photometry - physical parameterization.

A Point Source Point Lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens mass and positions and proper motions of both the lens and source.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

mL: float

Mass of the lens (Msun)

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

beta: float

Angular distance between the lens and source on the plane of the sky (mas). Can be

• positive (u0_amp > 0 when u0_hat[0] < 0) or

• negative (u0_amp < 0 when u0_hat[0] > 0).

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

Ratio of Distance from the obersver to the lens to Distance from the observer to the source

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is assumed to be luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_LumLens_Par_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax_LumLens, PSPL_PhotAstromParam2

PSPL model for photometry and astrometry – photom-like parameterization

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is assumed to be luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_LumLens_Par_Param4(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax_LumLens, PSPL_PhotAstromParam4

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is assumed to be luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL_parallax2 / PSPL_multiphot_parallax

class model.PSPL_PhotAstrom_Par_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax, PSPL_PhotAstromParam2

PSPL model for photometry and astrometry – photom-like parameterization

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_noPar_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_noParallax, PSPL_PhotAstromParam2

PSPL model for photometry and astrometry – photom-like parameterization

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t)	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Not supported on this object.

get_amplification(t)

Get an array of the photometric amplifications at the input times. No parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. No parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax, PSPL_PhotAstromParam3

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam4 except it fits for log10(thetaE) instead of thetaE.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_Param4(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax, PSPL_PhotAstromParam4

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_noPar_Param4(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_noParallax, PSPL_PhotAstromParam4

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t)	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Not supported on this object.

get_amplification(t)

Get an array of the photometric amplifications at the input times. No parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. No parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Astrom_Par_Param4(*args, **kwargs)

Bases: ModelClassABC, PSPL_Astrom, PSPL_Parallax, PSPL_AstromParam4

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t_obs, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Astrom_Par_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_Astrom, PSPL_Parallax, PSPL_AstromParam3

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam3 except it fits only astrometry, no photometry.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

log10_thetaE: float

The log of the Einstein radius log10(thetaE/mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t_obs, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL_phot

class model.PSPL_Phot_noPar_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_Phot, PSPL_noParallax, PSPL_PhotParam1

PSPL model for photometry only.

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS).

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

get_astrometry
get_astrometry_unlensed
get_centroid_shift
get_lens_astrometry
get_resolved_amplification
get_resolved_astrometry
log_likely_astrometry

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Not supported on this object.

get_amplification(t)

Get an array of the photometric amplifications at the input times. No parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. No parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_noPar_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_Phot, PSPL_noParallax, PSPL_PhotParam2

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

get_astrometry
get_astrometry_unlensed
get_centroid_shift
get_lens_astrometry
get_resolved_amplification
get_resolved_astrometry
log_likely_astrometry

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Not supported on this object.

get_amplification(t)

Get an array of the photometric amplifications at the input times. No parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. No parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL_phot_parallax / PSPL_phot_multiphot_parallax

class model.PSPL_Phot_Par_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_Phot, PSPL_Parallax, PSPL_PhotParam1

PSPL model for photometry only.

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS).

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

get_astrometry
get_astrometry_unlensed
get_centroid_shift
get_lens_astrometry
get_resolved_amplification
get_resolved_astrometry
log_likely_astrometry
set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_Phot, PSPL_Parallax, PSPL_PhotParam2

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

get_astrometry
get_astrometry_unlensed
get_centroid_shift
get_lens_astrometry
get_resolved_amplification
get_resolved_astrometry
log_likely_astrometry
set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Phot parallax with GP

class model.PSPL_Phot_Par_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam1

PSPL model for photometry only.

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS).

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

get_astrometry
get_astrometry_unlensed
get_centroid_shift
get_lens_astrometry
get_resolved_amplification
get_resolved_astrometry
log_likely_astrometry
set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam2

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

get_astrometry
get_astrometry_unlensed
get_centroid_shift
get_lens_astrometry
get_resolved_amplification
get_resolved_astrometry
log_likely_astrometry
set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GP_Param1_2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam1_2

PSPL model for photometry only.

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS).

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

get_astrometry
get_astrometry_unlensed
get_centroid_shift
get_lens_astrometry
get_resolved_amplification
get_resolved_astrometry
log_likely_astrometry
set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GP_Param2_2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam2_2

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

get_astrometry
get_astrometry_unlensed
get_centroid_shift
get_lens_astrometry
get_resolved_amplification
get_resolved_astrometry
log_likely_astrometry
set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Phot, no parallax with GP

class model.PSPL_Phot_noPar_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_noParallax, PSPL_GP_PhotParam1

PSPL model for photometry only.

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS).

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

get_astrometry
get_astrometry_unlensed
get_centroid_shift
get_lens_astrometry
get_resolved_amplification
get_resolved_astrometry
log_likely_astrometry

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Not supported on this object.

get_amplification(t)

Get an array of the photometric amplifications at the input times. No parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. No parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_noPar_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_noParallax, PSPL_GP_PhotParam2

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

get_astrometry
get_astrometry_unlensed
get_centroid_shift
get_lens_astrometry
get_resolved_amplification
get_resolved_astrometry
log_likely_astrometry

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Not supported on this object.

get_amplification(t)

Get an array of the photometric amplifications at the input times. No parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. No parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL PhotAstrom, parallax with GP

class model.PSPL_PhotAstrom_Par_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam1

PSPL model for astrometry and photometry - physical parameterization.

A Point Source Point Lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens mass and positions and proper motions of both the lens and source.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

mL: float

Mass of the lens (Msun)

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

beta: float

Angular distance between the lens and source on the plane of the sky (mas). Can be

• positive (u0_amp > 0 when u0_hat[0] < 0) or

• negative (u0_amp < 0 when u0_hat[0] > 0).

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

Ratio of Distance from the obersver to the lens to Distance from the observer to the source

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam2

PSPL model for photometry and astrometry – photom-like parameterization

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GP_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam3

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam4 except it fits for log10(thetaE) instead of thetaE.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GP_Param4(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam4

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_LumLens_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax_LumLens, PSPL_GP_PhotAstromParam1

PSPL model for astrometry and photometry - physical parameterization.

A Point Source Point Lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens mass and positions and proper motions of both the lens and source.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

mL: float

Mass of the lens (Msun)

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

beta: float

Angular distance between the lens and source on the plane of the sky (mas). Can be

• positive (u0_amp > 0 when u0_hat[0] < 0) or

• negative (u0_amp < 0 when u0_hat[0] > 0).

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

Ratio of Distance from the obersver to the lens to Distance from the observer to the source

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is assumed to be luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_LumLens_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax_LumLens, PSPL_GP_PhotAstromParam2

PSPL model for photometry and astrometry – photom-like parameterization

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is assumed to be luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_LumLens_GP_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax_LumLens, PSPL_GP_PhotAstromParam3

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam4 except it fits for log10(thetaE) instead of thetaE.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is assumed to be luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_LumLens_GP_Param4(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax_LumLens, PSPL_GP_PhotAstromParam4

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t_obs[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t_obs)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

get_amplification(t)

Get an array of the photometric amplifications at the input times. Parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t_obs, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is assumed to be luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t_obs)

Get the astrometry of the source if the lens didn’t exist. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included and the lens is luminous. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t_obs)

Get the astrometry for the foreground lens at the input times. Parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. Parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. Parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL PhotAstrom, no parallax with GP

class model.PSPL_PhotAstrom_noPar_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_noParallax, PSPL_GP_PhotAstromParam1

PSPL model for astrometry and photometry - physical parameterization.

A Point Source Point Lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens mass and positions and proper motions of both the lens and source.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

mL: float

Mass of the lens (Msun)

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

beta: float

Angular distance between the lens and source on the plane of the sky (mas). Can be

• positive (u0_amp > 0 when u0_hat[0] < 0) or

• negative (u0_amp < 0 when u0_hat[0] > 0).

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

Ratio of Distance from the obersver to the lens to Distance from the observer to the source

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t)	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Not supported on this object.

get_amplification(t)

Get an array of the photometric amplifications at the input times. No parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. No parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_noPar_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_noParallax, PSPL_GP_PhotAstromParam2

PSPL model for photometry and astrometry – photom-like parameterization

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_amplification(t)	Get an array of the photometric amplifications at the input times.
get_astrometry(t[, ast_filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t)	Get the astrometry of the source if the lens didn't exist.
get_centroid_shift(t)	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t)	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx, print_warning])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t)	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic()

Not supported on this object.

get_amplification(t)

Get an array of the photometric amplifications at the input times. No parallax is included.

Parameters:

tarray_like

Array of times in MJD.DDD

get_astrometry(t, ast_filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

ast_filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry_unlensed(t)

Get the astrometry of the source if the lens didn’t exist. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_centroid_shift(t)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

get_photometry(t, filt_idx=0, print_warning=True)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

Other Parameters:

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_index] = False.

Parameters:

t_obsarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t_obs.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. No parallax is included. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t_obs.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t_obs.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t_obs.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t_obs.

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

t_obsarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t_obs.

mag_obs_errarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t_obs.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.