Parameterization Class Family

Here is a subsection of the inheritance diagram for the PSPL Parametrization classes showing the AstromParam, PhotParam, and PhotAstromParam structures.

PSPL Models

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

Bases: ABC

An abstract class that all Param classes should sub-class. This serves as a reminder for the class variables that MUST be set.

class model.PSPL_AstromParam4(t0, u0_amp, tE, thetaE, piS, piE_E, piE_N, xS0_E, xS0_N, muS_E, muS_N, raL=None, decL=None)

Bases: PSPL_Param

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

Notes

Note

Required parameters if calculating with parallax

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

• decL: Declination of the lens in decimal degrees.

Attributes

t0: float

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

u0_amp: float

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

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

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

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

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

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

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

xS0_N: float

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

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

class model.PSPL_AstromParam3(t0, u0_amp, tE, log10_thetaE, piS, piE_E, piE_N, xS0_E, xS0_N, muS_E, muS_N, raL=None, decL=None)

Bases: PSPL_Param

DESCRIPTION: Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam3 except it fits only astrometry, no photometry.

Notes

Note

Required parameters if calculating with parallax

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

• decL: Declination of the lens in decimal degrees.

Attributes

t0: float

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

u0_amp: float

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

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

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

tE: float

Einstein crossing time (days).

log10_thetaE: float

The log of the Einstein radius log10(thetaE/mas).

piS: float

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

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

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

xS0_N: float

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

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

class model.PSPL_PhotParam1(t0, u0_amp, tE, piE_E, piE_N, b_sff, mag_src, raL=None, decL=None)

Bases: PSPL_Param

PSPL model for photometry only.

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS).

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

Attributes

t0: float

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

u0_amp: float

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

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

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

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

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

mag_src: numpy array or list

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

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

class model.PSPL_PhotParam2(t0, u0_amp, tE, piE_E, piE_N, b_sff, mag_base, raL=None, decL=None)

Bases: PSPL_Param

DESCRIPTION: Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Notes

Note

Required parameters if calculating with parallax

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

• decL: Declination of the lens in decimal degrees.

Attributes

t0: float

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

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

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

mag_base: numpy array or list

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

class model.PSPL_PhotAstromParam1(mL, t0, beta, dL, dL_dS, xS0_E, xS0_N, muL_E, muL_N, muS_E, muS_N, b_sff, mag_src, raL=None, decL=None)

Bases: PSPL_Param

PSPL model for astrometry and photometry - physical parameterization.

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

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

Attributes

mL: float

Mass of the lens (Msun)

t0: float

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

beta: float

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

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

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

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

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

xS0_E: float

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

xS0_N: float

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

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

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

mag_src: numpy array or list

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

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

class model.PSPL_PhotAstromParam2(t0, u0_amp, tE, thetaE, piS, piE_E, piE_N, xS0_E, xS0_N, muS_E, muS_N, b_sff, mag_src, raL=None, decL=None)

Bases: PSPL_Param

PSPL model for photometry and astrometry – photom-like parameterization

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

Attributes

t0: float

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

u0_amp: float

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

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

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

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

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

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

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

xS0_N: float

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

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

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

mag_src: numpy array or list

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

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

class model.PSPL_PhotAstromParam3(t0, u0_amp, tE, log10_thetaE, piS, piE_E, piE_N, xS0_E, xS0_N, muS_E, muS_N, b_sff, mag_base, raL=None, decL=None)

Bases: PSPL_Param

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

Notes

Note

Required parameters if calculating with parallax

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

• decL: Declination of the lens in decimal degrees.

Attributes

t0float

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

u0_ampfloat

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

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

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

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

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

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

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

xS0_Nfloat

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

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

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

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

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

mag_basenumpy array or list

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

class model.PSPL_PhotAstromParam4(t0, u0_amp, tE, thetaE, piS, piE_E, piE_N, xS0_E, xS0_N, muS_E, muS_N, b_sff, mag_base, raL=None, decL=None)

Bases: PSPL_Param

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

Parameters

t0float

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

u0_ampfloat

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

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

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

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

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

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

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

xS0_Nfloat

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

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

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

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

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

mag_basenumpy array or list

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

Notes

Note

Required parameters if calculating with parallax

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

• decL: Declination of the lens in decimal degrees.

class model.PSPL_PhotAstromParam5(t0, u0_amp, tE, log10_thetaE, piS, piE_E, piEN_piEE, xS0_E, xS0_N, muS_E, muS_N, b_sff, mag_base, raL=None, decL=None)

Bases: PSPL_Param

DESCRIPTION: Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It fits for piEN/piEE and piEE, instead of piEE and piEN.

Notes

Note

Required parameters if calculating with parallax

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

• decL: Declination of the lens in decimal degrees.

Attributes

t0float

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

u0_ampfloat

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

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

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

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

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

piEN_piEEfloat

Ratio of piE_N to piE_E.

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

xS0_Efloat

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

xS0_Nfloat

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

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

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

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

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

mag_basenumpy array or list

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

GP Models

class model.PSPL_GP_PhotParam1(t0, u0_amp, tE, piE_E, piE_N, b_sff, mag_src, gp_log_sigma, gp_log_rho, gp_log_S0, gp_log_omega0, raL=None, decL=None)

Bases: PSPL_PhotParam1

class model.PSPL_GP_PhotParam1_2(t0, u0_amp, tE, piE_E, piE_N, b_sff, mag_src, gp_log_sigma, gp_rho, gp_log_omega04_S0, gp_log_omega0, raL=None, decL=None)

Bases: PSPL_PhotParam1

Figuring out the new prior parametrization.

class model.PSPL_GP_PhotParam2(t0, u0_amp, tE, piE_E, piE_N, b_sff, mag_base, gp_log_sigma, gp_log_rho, gp_log_S0, gp_log_omega0, raL=None, decL=None)

Bases: PSPL_PhotParam2

class model.PSPL_GP_PhotParam2_2(t0, u0_amp, tE, piE_E, piE_N, b_sff, mag_base, gp_log_sigma, gp_rho, gp_log_omega04_S0, gp_log_omega0, raL=None, decL=None)

Bases: PSPL_PhotParam2

class model.PSPL_GP_PhotAstromParam1(mL, t0, beta, dL, dL_dS, xS0_E, xS0_N, muL_E, muL_N, muS_E, muS_N, b_sff, mag_src, gp_log_sigma, gp_rho, gp_log_omega04_S0, gp_log_omega0, raL=None, decL=None)

Bases: PSPL_PhotAstromParam1

class model.PSPL_GP_PhotAstromParam2(t0, u0_amp, tE, thetaE, piS, piE_E, piE_N, xS0_E, xS0_N, muS_E, muS_N, b_sff, mag_src, gp_log_sigma, gp_rho, gp_log_omega04_S0, gp_log_omega0, raL=None, decL=None)

Bases: PSPL_PhotAstromParam2

class model.PSPL_GP_PhotAstromParam2(t0, u0_amp, tE, thetaE, piS, piE_E, piE_N, xS0_E, xS0_N, muS_E, muS_N, b_sff, mag_src, gp_log_sigma, gp_rho, gp_log_omega04_S0, gp_log_omega0, raL=None, decL=None)

Bases: PSPL_PhotAstromParam2

class model.PSPL_GP_PhotAstromParam3(t0, u0_amp, tE, log10_thetaE, piS, piE_E, piE_N, xS0_E, xS0_N, muS_E, muS_N, b_sff, mag_base, gp_log_sigma, gp_rho, gp_log_omega04_S0, gp_log_omega0, raL=None, decL=None)

Bases: PSPL_PhotAstromParam3

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

Notes

Note

raL and decL are required parameters if calculating with parallax

Attributes

t0: float

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

u0_amp: float

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

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

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

tE: float

Einstein crossing time (days).

log10_thetaE: float

log10 of the size of the Einstein radius in (mas).

piS: float

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

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

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

xS0_N: float

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

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list of floats

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

mag_base: numpy array or list of floats

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

gp_log_sigma: float

Guassian process \(log(\sigma)\) for the Matern 3/2 kernel.

gp_rho: float

Guassian process \({\rho}\) for the Matern 3/2 kernel.

gp_log_omega04_S0: float

Guassian process \(log(\omega_0^4 * S_0)\) from the SHO kernel.

gp_log_omega0: float

Guassian process \(log(\omega_0)\) from the SHO kernel.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

class model.PSPL_GP_PhotAstromParam4(t0, u0_amp, tE, thetaE, piS, piE_E, piE_N, xS0_E, xS0_N, muS_E, muS_N, b_sff, mag_base, gp_log_sigma, gp_rho, gp_log_omega04_S0, gp_log_omega0, raL=None, decL=None)

Bases: PSPL_PhotAstromParam4

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

Notes

Note

raL and decL are required parameters if calculating with parallax

For an explanation of the Guassian process parameters, see Golovich et al. 2019()

Attributes

t0: float

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

u0_amp: float

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

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

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

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

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

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

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

xS0_N: float

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

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: float

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

mag_base: float

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

gp_log_sigma: float

Guassian process \(log(\sigma)\) for the Matern 3/2 kernel.

gp_rho: float

Guassian process \({\rho}\) for the Matern 3/2 kernel.

gp_log_omega04_S0: float

Guassian process \(log(\omega_0^4 * S_0)\) from the SHO kernel.

gp_log_omega0: float

Guassian process \(log(\omega_0)\) from the SHO kernel.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.