FSPL(Finite-Source Point Lens) Models - NOT DONE YET… place holders

FSPL Classes

class model.FSPL_PhotAstrom

Bases: FSPL, PSPL_PhotAstrom

Contains methods for model a PSPL photometry + astrometry. This is a Data-type class in our hierarchy. It is abstract and should not be instantiated.

Attributes:

Available class variables that should be defined.

t0

tE

u0_amp

u0_E

u0_N

beta

piE_E - valid only if parallax model

piE_N - valid only if parallax model

piE_amp

mL

thetaE_amp

thetaE_E

thetaE_N

xS0_E

xS0_N

xL0_E

xL0_N

muS_E

muS_N

muL_E

muL_N

muRel_E

muRel_N

muRel_amp

piS

piL

dL

dS

dL_dS (dL over dS)

radius

n

b_sff[#]

mag_src[#] – add in

mag_base[#] – add in

raL - if parallax model

decL - if parallax model

Methods

animate(crossings, time_steps, frame_time, ...)	Produces animation of microlensing event.
get_all_arrays(t_obs)	Obtain the image and amplitude arrays for each t_obs.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_outline_unlensed(t_obs)	Get the astrometry of the source outline if the lens didn't exist.
get_chi2_astrometry(t_obs, x_obs, y_obs, ...)	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t_obs, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for the combined source images.
get_resolved_amplification(t_obs[, ...])	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed (lensed) source position on the sky.
get_resolved_astrometry_outline(t_obs)	Get the x, y astrometry for each of the two lensed source images and all the associated outline points.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
get_source_outline_astrometry(center)	Return astrometric points that outline the outer circumference of the source star.
get_u(t_obs)	Get the separation vector,
get_u_outline(t_obs)	Get the separation vector,
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_obs, ...[, ...])	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

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

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

Parameters:

tE:

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

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

time_steps:

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

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

get_all_arrays(t_obs)

Obtain the image and amplitude arrays for each t_obs. These arrays contain the positions for each point in the outline for each lensed image.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of positions of each lensed image at each t_obs. Shape = [len(t_obs), n_images=2, [E,N]] The last axis contains East and North positions on the sky in arcseconds.

amp_arrarray_like

Array/tuple of amplification of each lensed image at each t_obs. Shape = [len(t_obs), n_images=2]

Notes

The algorithm uses green’s theorem to change an area integral of the image of the source into a path integral around the outside outline. We perform a first-order contour integral to approximate the area.

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

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

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). 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.

get_astrometry_outline_unlensed(t_obs)

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

get_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for the combined source images.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of the centroid at t_obs.

Other Parameters:

amp_arrarray_like

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

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

get_resolved_amplification(t_obs, filt_idx=0, amp_arr=None)

Get the photometric amplification term at a set of times, t for both the plus and minus images.

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed (lensed) source position on the sky.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images=2, 2]

Array of vector positions of the centroid at each t_obs. Last axis contains East/North positions.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs, [E,N]).

amp_arrarray_like

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

get_resolved_astrometry_outline(t_obs)

Get the x, y astrometry for each of the two lensed source images and all the associated outline points. The two lensed source images are labeled plus and minus.

These are actual positions on the sky.

Returns:

[xS_plus, xS_minus]list of numpy arrays

xS_plus is the vector position of the plus image. xS_minus is the vector position of the plus image. Each shape = [len(t_obs), self.n_outline, 2] where the last axis contains East and North positions.

get_resolved_photometry(t_obs, 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:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [2, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image and each outline point for that image at each time, i.e. amp_arr.shape = (len(t_obs), self.n_outline, number of images at each t_obs).

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

filt_idxint

The filter index (def=0).

get_u(t_obs)

Get the separation vector,

ec{u}(t), which is the unlensed

source - lens separation vector on the plane of the sky in units of heta_E.

get_u_outline(t_obs)

Get the separation vector,

ec{u}(t), which is the unlensed

source - lens separation vector for each point of the source outline. Positions are on the plane of the sky in units of heta_E.