BSBL Model Classes

BSBL Photometry + Astrometry with Static Lens Secondary

class model.BSBL_PhotAstrom_Par_Param1(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_Parallax, BSBL_PhotAstromParam1

Parameterization with t0 defined between the geometric center of the lens and the source. Parallax.

BSBL model for astrometry and photometry - physical parameterization.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions. Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0float

Time of closest approach between the geometric center of source and geometric center of the lens, as seen from Earth (MJD.DDD)

xS0_Efloat

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

xS0_Nfloat

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

beta: float

Angular distance between the source PRIMARY position and the GEOMETRIC center of the lenses 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

sepLfloat

Angular separation of the lens secondary from the lens primary (mas).

alphaLfloat

Angle made between the binary lens axis and North; measured in degrees East of North. Example, alphaL = 90 will place the lens primary to the East and the lens secondary to the West.

sepSfloat

Angular separation of the source secondary from the source primary (mas).

alphaSfloat

Angle made between the binary source axis and North; measured in degrees East of North. Example, alphaL = 90 will place the source primary to the East and the source secondary to the West.

mag_src_pri: array or list

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

mag_src_sec: array or list

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

b_sffnumpy array or list

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

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

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

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.BSBL_PhotAstrom_Par_Param2(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_Parallax, BSBL_PhotAstromParam2

Parameterization with t0 defined between the geometric center of the source and the primary lens. Parallax.

BSBL model for astrometry and photometry - physical parameterization

with primary lens and primary source center.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions. Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0_pfloat

Time of closest approach between source and PRIMARY LENS (MJD.DDD)

xS0_Efloat

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

xS0_Nfloat

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

beta_pfloat

Angular distance between the source PRIMARY position and the PRIMARY center of the lenses 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

sepLfloat

Angular separation of the lens secondary from the lens primary (mas).

alphaLfloat

Angle made between the binary lens axis and North; measured in degrees East of North. Example, alphaL = 90 will place the lens primary to the East and the lens secondary to the West.

sepSfloat

Angular separation of the source secondary from the source primary (mas).

alphaSfloat

Angle made between the binary source axis and North; measured in degrees East of North. Example, alphaL = 90 will place the source primary to the East and the source secondary to the West.

mag_src_pri: array or list

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

mag_src_sec: array or list

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

b_sffnumpy array or list

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

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

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

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.BSBL_PhotAstrom_noPar_Param1(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_noParallax, BSBL_PhotAstromParam1

Parameterization with t0 defined between the geometric center of the lens and the source; takes in lens masses; No Parallax.

BSBL model for astrometry and photometry - physical parameterization.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions. Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0float

Time of closest approach between the geometric center of source and geometric center of the lens, as seen from Earth (MJD.DDD)

xS0_Efloat

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

xS0_Nfloat

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

beta: float

Angular distance between the source PRIMARY position and the GEOMETRIC center of the lenses 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

sepLfloat

Angular separation of the lens secondary from the lens primary (mas).

alphaLfloat

Angle made between the binary lens axis and North; measured in degrees East of North. Example, alphaL = 90 will place the lens primary to the East and the lens secondary to the West.

sepSfloat

Angular separation of the source secondary from the source primary (mas).

alphaSfloat

Angle made between the binary source axis and North; measured in degrees East of North. Example, alphaL = 90 will place the source primary to the East and the source secondary to the West.

mag_src_pri: array or list

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

mag_src_sec: array or list

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

b_sffnumpy array or list

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

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

Not supported on this object.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.BSBL_PhotAstrom_noPar_Param2(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_noParallax, BSBL_PhotAstromParam2

Parameterization with t0 defined between the geometric center of the source and the primary lens. No Parallax.

BSBL model for astrometry and photometry - physical parameterization

with primary lens and primary source center.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions. Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0_pfloat

Time of closest approach between source and PRIMARY LENS (MJD.DDD)

xS0_Efloat

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

xS0_Nfloat

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

beta_pfloat

Angular distance between the source PRIMARY position and the PRIMARY center of the lenses 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

sepLfloat

Angular separation of the lens secondary from the lens primary (mas).

alphaLfloat

Angle made between the binary lens axis and North; measured in degrees East of North. Example, alphaL = 90 will place the lens primary to the East and the lens secondary to the West.

sepSfloat

Angular separation of the source secondary from the source primary (mas).

alphaSfloat

Angle made between the binary source axis and North; measured in degrees East of North. Example, alphaL = 90 will place the source primary to the East and the source secondary to the West.

mag_src_pri: array or list

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

mag_src_sec: array or list

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

b_sffnumpy array or list

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

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

Not supported on this object.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

BSBL Photometry + Astrometry, Circular Orbits for Lens

class model.BSBL_PhotAstrom_Par_CircOrbs_Param1(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_Parallax, BSBL_PhotAstrom_CircOrbs_Param1

Parameterization with t0 defined between the primary source and binary lens CoM. Takes in masses of lenses. Parallax.

BSBL model for astrometry and photometry - physical parameterization.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions.

Note that this is a non-STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0_comfloat

Time of closest approach between source COM and Lens COM (MJD.DDD)

xS0_Efloat

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

xS0_Nfloat

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

beta: float

Angular distance between the primary source and the lens geometric center 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

omegaL_pri: float

The argument of periastron of the primary lens’s orbit in degrees.

big_omegaL_sec: float

The longitude of the ascending node of the secondary lens’s orbit in degrees.

iL: float

Inclination angle of the system in degrees.

eL: float

Eccentricity of the Lens System

tpL: float

This is the time of the periastron of the system in days.

aL: float

This is the semi-major axis of the binary lens system (mas)

omegaS_pri: float

The argument of periastron of the primary source’s orbit in degrees.

big_omegaS_sec: float

The longitude of the ascending node of the secondary source’s orbit in degrees.

is: float

Inclination angle of the system in degrees.

eS: float

Eccentricity of the Source System

pS: float

Orbital period of the system in days.

tpS: float

This is the time of the periastron of the system in days.

alephS: float

This is the semi-major axis of the primary source in mas.

aleph_secS: float

This is the semi-major axis of the secondary source in mas.

mag_src_pri: array or list

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

mag_src_sec: array or list

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

b_sffnumpy array or list

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

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’])

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

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

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.BSBL_PhotAstrom_Par_CircOrbs_Param2(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_Parallax, BSBL_PhotAstrom_CircOrbs_Param2

Parameterization with t0 and u0_amp_com defined between the primary source and binary lens center of mass. Takes in mass ratio of lenses. Parallax.

BSBL model for astrometry and photometry - physical parameterization.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions.

Note that this is a non-STATIC binary lens, i.e. there is no orbital motion.

Attributes:

t0_comfloat

Time of closest approach between the primary source and lens COM (MJD.DDD)

u0_amp_com: float

Angular distance between the primary source and the binary lens center of mass 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).

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

qfloat

Mass ratio (M2 / M1)

xS0_Efloat

R.A. of primary source position on sky at t = t0_com (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

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

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

omegaL_pri: float

The argument of periastron of the primary lens’s orbit in degrees.

big_omegaL_sec: float

The longitude of the ascending node of the secondary lens’s orbit in degrees.

iL: float

Inclination angle of the system in degrees.

eL: float

Eccentricity of the Lens System

tpL: float

This is the time of the periastron of the system in days.

aL: float

This is the semi-major axis of the binary lens system (mas)

omegaS_pri: float

The argument of periastron of the primary source’s orbit in degrees.

big_omegaS_sec: float

The longitude of the ascending node of the secondary source’s orbit in degrees.

is: float

Inclination angle of the system in degrees.

eS: float

Eccentricity of the Source System

pS: float

Orbital period of the system in days.

tpS: float

This is the time of the periastron of the system in days.

alephS: float

This is the semi-major axis of the primary source in mas.

aleph_secS: float

This is the semi-major axis of the secondary source in mas.

fratio_bin: float

Flux ratio of secondary flux / primary flux.

mag_basearray or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter. Note that \(flux_{base} = f_{src1} + f_{src2} + f_{blend}\) such that \(b_sff = (f_{src1}+ f_{src2}) / ( f_{src1} + f_{src2} + f_{blend} )\)

b_sffarray or list

The ratio of the source flux to the total (source + neighbors + lens):math:b_sff = (f_{S1} + f_{S2}) / (f_{S1} + f_{s2} + f_L + f_N). This must be passed in as a list or array, with one entry for each photometric filter.

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’])

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

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

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.BSBL_PhotAstrom_noPar_CircOrbs_Param1(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_noParallax, BSBL_PhotAstrom_CircOrbs_Param1

Parameterization with t0 defined between the primary source and binary lens CoM. Takes in masses of lenses. No Parallax.

BSBL model for astrometry and photometry - physical parameterization.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions.

Note that this is a non-STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0_comfloat

Time of closest approach between source COM and Lens COM (MJD.DDD)

xS0_Efloat

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

xS0_Nfloat

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

beta: float

Angular distance between the primary source and the lens geometric center 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

omegaL_pri: float

The argument of periastron of the primary lens’s orbit in degrees.

big_omegaL_sec: float

The longitude of the ascending node of the secondary lens’s orbit in degrees.

iL: float

Inclination angle of the system in degrees.

eL: float

Eccentricity of the Lens System

tpL: float

This is the time of the periastron of the system in days.

aL: float

This is the semi-major axis of the binary lens system (mas)

omegaS_pri: float

The argument of periastron of the primary source’s orbit in degrees.

big_omegaS_sec: float

The longitude of the ascending node of the secondary source’s orbit in degrees.

is: float

Inclination angle of the system in degrees.

eS: float

Eccentricity of the Source System

pS: float

Orbital period of the system in days.

tpS: float

This is the time of the periastron of the system in days.

alephS: float

This is the semi-major axis of the primary source in mas.

aleph_secS: float

This is the semi-major axis of the secondary source in mas.

mag_src_pri: array or list

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

mag_src_sec: array or list

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

b_sffnumpy array or list

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

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’])

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

Not supported on this object.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.BSBL_PhotAstrom_noPar_CircOrbs_Param2(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_noParallax, BSBL_PhotAstrom_CircOrbs_Param2

Parameterization with t0 and u0_amp_com defined between the primary source and binary lens center of mass. Takes in mass ratio of lenses. No Parallax.

BSBL model for astrometry and photometry - physical parameterization.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions.

Note that this is a non-STATIC binary lens, i.e. there is no orbital motion.

Attributes:

t0_comfloat

Time of closest approach between the primary source and lens COM (MJD.DDD)

u0_amp_com: float

Angular distance between the primary source and the binary lens center of mass 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).

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

qfloat

Mass ratio (M2 / M1)

xS0_Efloat

R.A. of primary source position on sky at t = t0_com (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

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

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

omegaL_pri: float

The argument of periastron of the primary lens’s orbit in degrees.

big_omegaL_sec: float

The longitude of the ascending node of the secondary lens’s orbit in degrees.

iL: float

Inclination angle of the system in degrees.

eL: float

Eccentricity of the Lens System

tpL: float

This is the time of the periastron of the system in days.

aL: float

This is the semi-major axis of the binary lens system (mas)

omegaS_pri: float

The argument of periastron of the primary source’s orbit in degrees.

big_omegaS_sec: float

The longitude of the ascending node of the secondary source’s orbit in degrees.

is: float

Inclination angle of the system in degrees.

eS: float

Eccentricity of the Source System

pS: float

Orbital period of the system in days.

tpS: float

This is the time of the periastron of the system in days.

alephS: float

This is the semi-major axis of the primary source in mas.

aleph_secS: float

This is the semi-major axis of the secondary source in mas.

fratio_bin: float

Flux ratio of secondary flux / primary flux.

mag_basearray or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter. Note that \(flux_{base} = f_{src1} + f_{src2} + f_{blend}\) such that \(b_sff = (f_{src1}+ f_{src2}) / ( f_{src1} + f_{src2} + f_{blend} )\)

b_sffarray or list

The ratio of the source flux to the total (source + neighbors + lens):math:b_sff = (f_{S1} + f_{S2}) / (f_{S1} + f_{s2} + f_L + f_N). This must be passed in as a list or array, with one entry for each photometric filter.

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’])

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

Not supported on this object.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

BSBL Photometry + Astrometry, Elliptical Orbits for Lens

class model.BSBL_PhotAstrom_Par_EllOrbs_Param1(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_Parallax, BSBL_PhotAstrom_EllOrbs_Param1

Parameterization with t0 defined between the lens CoM and source CoM. Takes in lens masses. Parallax.

BSBL model for astrometry and photometry - physical parameterization.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions.

Note that this is a non-STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0_comfloat

Time of closest approach between source COM and Lens COM (MJD.DDD)

xS0_Efloat

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

xS0_Nfloat

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

beta: float

Angular distance between the primary source and the lens geometric center 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

omegaL_pri: float

The argument of periastron of the primary lens’s orbit in degrees.

big_omegaL_sec: float

The longitude of the ascending node of the secondary lens’s orbit in degrees.

iL: float

Inclination angle of the system in degrees.

eL: float

Eccentricity of the Lens System

tpL: float

This is the time of the periastron of the system in days.

aL: float

This is the semi-major axis of the binary lens system (mas)

omegaS_pri: float

The argument of periastron of the primary source’s orbit in degrees.

big_omegaS_sec: float

The longitude of the ascending node of the secondary source’s orbit in degrees.

is: float

Inclination angle of the system in degrees.

eS: float

Eccentricity of the Source System

pS: float

Orbital period of the system in days.

tpS: float

This is the time of the periastron of the system in days.

alephS: float

This is the semi-major axis of the primary source in mas.

aleph_secS: float

This is the semi-major axis of the secondary source in mas.

mag_src_pri: array or list

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

mag_src_sec: array or list

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

b_sffnumpy array or list

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

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’])

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

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

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.BSBL_PhotAstrom_Par_EllOrbs_Param2(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_Parallax, BSBL_PhotAstrom_EllOrbs_Param2

Parameterization with t0 defined between the primary source and binary lens CoM. Takes in mass ratio of lenses. Parallax.

BSBL model for astrometry and photometry - physical parameterization.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions.

Note that this is a non-STATIC binary lens, i.e. there is no orbital motion.

Attributes:

t0_comfloat

Time of closest approach between the primary source and lens COM (MJD.DDD)

u0_amp_com: float

Angular distance between the primary source and the binary lens center of mass 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).

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

qfloat

Mass ratio (M2 / M1)

xS0_Efloat

R.A. of primary source position on sky at t = t0_com (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

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

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

omegaL_pri: float

The argument of periastron of the primary lens’s orbit in degrees.

big_omegaL_sec: float

The longitude of the ascending node of the secondary lens’s orbit in degrees.

iL: float

Inclination angle of the system in degrees.

eL: float

Eccentricity of the Lens System

tpL: float

This is the time of the periastron of the system in days.

aL: float

This is the semi-major axis of the binary lens system (mas)

omegaS_pri: float

The argument of periastron of the primary source’s orbit in degrees.

big_omegaS_sec: float

The longitude of the ascending node of the secondary source’s orbit in degrees.

is: float

Inclination angle of the system in degrees.

eS: float

Eccentricity of the Source System

pS: float

Orbital period of the system in days.

tpS: float

This is the time of the periastron of the system in days.

alephS: float

This is the semi-major axis of the primary source in mas.

aleph_secS: float

This is the semi-major axis of the secondary source in mas.

fratio_bin: float

Flux ratio of secondary flux / primary flux.

mag_basearray or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter. Note that \(flux_{base} = f_{src1} + f_{src2} + f_{blend}\) such that \(b_sff = (f_{src1}+ f_{src2}) / ( f_{src1} + f_{src2} + f_{blend} )\)

b_sffarray or list

The ratio of the source flux to the total (source + neighbors + lens):math:b_sff = (f_{S1} + f_{S2}) / (f_{S1} + f_{s2} + f_L + f_N). This must be passed in as a list or array, with one entry for each photometric filter.

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’])

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

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

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.BSBL_PhotAstrom_noPar_EllOrbs_Param1(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_noParallax, BSBL_PhotAstrom_EllOrbs_Param1

Parameterization with t0 defined between the lens CoM and source CoM. Takes in lens masses. No Parallax.

BSBL model for astrometry and photometry - physical parameterization.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions.

Note that this is a non-STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0_comfloat

Time of closest approach between source COM and Lens COM (MJD.DDD)

xS0_Efloat

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

xS0_Nfloat

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

beta: float

Angular distance between the primary source and the lens geometric center 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

omegaL_pri: float

The argument of periastron of the primary lens’s orbit in degrees.

big_omegaL_sec: float

The longitude of the ascending node of the secondary lens’s orbit in degrees.

iL: float

Inclination angle of the system in degrees.

eL: float

Eccentricity of the Lens System

tpL: float

This is the time of the periastron of the system in days.

aL: float

This is the semi-major axis of the binary lens system (mas)

omegaS_pri: float

The argument of periastron of the primary source’s orbit in degrees.

big_omegaS_sec: float

The longitude of the ascending node of the secondary source’s orbit in degrees.

is: float

Inclination angle of the system in degrees.

eS: float

Eccentricity of the Source System

pS: float

Orbital period of the system in days.

tpS: float

This is the time of the periastron of the system in days.

alephS: float

This is the semi-major axis of the primary source in mas.

aleph_secS: float

This is the semi-major axis of the secondary source in mas.

mag_src_pri: array or list

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

mag_src_sec: array or list

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

b_sffnumpy array or list

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

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’])

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

Not supported on this object.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.BSBL_PhotAstrom_noPar_EllOrbs_Param2(*args, **kwargs)

Bases: ModelClassABC, BSBL_PhotAstrom, BSBL_noParallax, BSBL_PhotAstrom_EllOrbs_Param2

Parameterization with t0 defined between the primary source and binary lens CoM. Takes in mass ratio of lenses. Parallax.

BSBL model for astrometry and photometry - physical parameterization.

A binary source binary lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens masses and positions and proper motions.

Note that this is a non-STATIC binary lens, i.e. there is no orbital motion.

Attributes:

t0_comfloat

Time of closest approach between the primary source and lens COM (MJD.DDD)

u0_amp_com: float

Angular distance between the primary source and the binary lens center of mass 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).

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

qfloat

Mass ratio (M2 / M1)

xS0_Efloat

R.A. of primary source position on sky at t = t0_com (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

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

muS_Efloat

Source system proper motion in the RA direction (mas/yr)

muS_Nfloat

Source system proper motion in the Dec. direction (mas/yr)

omegaL_pri: float

The argument of periastron of the primary lens’s orbit in degrees.

big_omegaL_sec: float

The longitude of the ascending node of the secondary lens’s orbit in degrees.

iL: float

Inclination angle of the system in degrees.

eL: float

Eccentricity of the Lens System

tpL: float

This is the time of the periastron of the system in days.

aL: float

This is the semi-major axis of the binary lens system (mas)

omegaS_pri: float

The argument of periastron of the primary source’s orbit in degrees.

big_omegaS_sec: float

The longitude of the ascending node of the secondary source’s orbit in degrees.

is: float

Inclination angle of the system in degrees.

eS: float

Eccentricity of the Source System

pS: float

Orbital period of the system in days.

tpS: float

This is the time of the periastron of the system in days.

alephS: float

This is the semi-major axis of the primary source in mas.

aleph_secS: float

This is the semi-major axis of the secondary source in mas.

fratio_bin: float

Flux ratio of secondary flux / primary flux.

mag_basearray or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter. Note that \(flux_{base} = f_{src1} + f_{src2} + f_{blend}\) such that \(b_sff = (f_{src1}+ f_{src2}) / ( f_{src1} + f_{src2} + f_{blend} )\)

b_sffarray or list

The ratio of the source flux to the total (source + neighbors + lens):math:b_sff = (f_{S1} + f_{S2}) / (f_{S1} + f_{s2} + f_L + f_N). This must be passed in as a list or array, with one entry for each photometric filter.

dmag_Lp_Lsnumpy array or list

Magnitude difference of lens primary - lens secondary. If the primary lens is dark, then dmag_L1_L2 should be set to 20 (or some other large, positive number). If the secondary lens 2 is dark, then it should be set to -20. Note, in astrometric filters, we assume all the excess flux (i.e. 1 - b_sff) comes from the lenses, not any neighbors.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’])

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_all_arrays(t[, filt_idx, check_sols, ...])	Obtain the image and amplitude arrays for each t.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t[, filt_idx, amp_arr])	Get the photometric amplification term at a set of times, t.
get_astrometry(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
get_caustics(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
get_centroid_shift(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_chi2_astrometry(t, 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, 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_complex_pos(t[, filt_idx])	Get the positions of the lenses and sources as complex numbers.
get_critical_curves(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_origin_astrometry(t[, filt_idx])	Equation of motion for just the foreground lens system.
get_lens_photometry([filt_idx])	Get the combined lens photometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, image_arr, ...])	Parallax: For each source, get the x, y astrometry for the multiple lensed source images.
get_resolved_lens_astrometry(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
get_resolved_lens_photometry([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
get_resolved_photometry(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
get_resolved_source_astrometry_unlensed(t[, ...])	Get the astrometry of the sources if the lens didn't exist.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])
lens_map(t, z)	Gets source plane position from lens plane position via the lens map.
log_likely_astrometry(t, 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, 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_photometry(t, mag_obs, mag_err_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, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, loc=None)

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(filt_idx=0)

Not supported on this object.

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t.

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t. shape = [N_times, N_sources, 5, 2]

amp_arrarray_like

Array/tuple of amplification of each images at each t. shape = [N_times, N_sources, 5]

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images for both sources.

Shape = [N_times, N_sources, N_solutions]

where [:, 0, :] is primary and [:, 1, :] is secondary.

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

Returns:

amp_arrarray_like

BLEH

get_amplification(t, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t.

Parameters:

t:

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_lensed

Returns flux-weighted average of lensed source positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = (N_times, N_sources, N_images). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat

Time to model.

N_ptsint, optional

Number of points to sample along the critical curve.

Returns:

w_arrarray_like

Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=0)

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

Parameters:

tarray_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.

mag_err_obsarray_like

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

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_complex_pos(t, filt_idx=0)

Get the positions of the lenses and sources as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

filt_idxint

Index of the filter or data set for the observing location array (needed for parallax).

Returns:

wcomplex array

Source positions (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat

Times to model.

N_ptsint, optional

Number of points to sample along the critical curve.

amp_invfloat, optional

Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like

Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the sources. Shape = [N_times, N_sources]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, N_sources

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_Lfloat

Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

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, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_like

Array of times to model.

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:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the multiple lensed source images. For each source, there can be up to 5 images. Sometimes there will be 3 and sometimes 5.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_resolvednumpy array

[shape = len(t), N_sources, N_images, 2] Array of vector positions of each lensed image.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t, i.e. image_arr.shape = [len(t), N_sources, N_images at each t]. Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

Notes

For each time t and each source, we have 3 or 5 images as a result of the binary lens.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s first lensed image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s second lensed image at the first time.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]

Position of the lens primary (arcsec)

xL2array_like, shape = [N_times, 2 directions]

Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional

Filter index.

Returns:

mag_L1, mag_L2float, float

Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

tarray_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t. Shape = [5, len(t)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t), number of images at each t).

This will over-ride t; but is more efficient when calculating both photometry and astrometry. If None, then just use t.

filt_idxint

The filter index (def=0).

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the sources if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]

The unlensed positions of the sources in arcseconds.

In other words,

xS[0, 0, :] returns the 2D sky position of the first source at the first time.

Similarly,

xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. 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).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

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

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Parameters:

tnumpy array

Times at which to evaluate the source-lens separation.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

unumpy array

Shape = [len(t), 2 sources, 2 directions on sky]

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like

Times to model. Shape = [N_times, 1]

zarray_like

Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like

Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, x_obs, y_obs, x_err_obs, y_err_obs, 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:

tarray_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.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

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, mag_obs, mag_err_obs, filt_idx=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:

tarray_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.

mag_err_obsarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.