MulensModel.pointlens module

MulensModel.pointlens.get_pspl_magnification(trajectory)

This is Paczynski equation, i.e., point-source–point-lens (PSPL) magnification.

Arguments :

trajectory: float, np.ndarray, or Trajectory object

The source-lens relative position. If _not_ a Trajectory object, then trajectory is assumed to be value(s) of \(u\).

Returns :

pspl_magnification: float or np.ndarray

The point-source–point-lens magnification for each point specified by trajectory.

class MulensModel.pointlens.PointLens(parameters=None)

Bases: object

Equations for calculating finite source effects for a point lens.

Keywords :

parameters: ModelParameters

Parameters of the model. Currently, only rho attribute is used.

Attributes :

parameters: ModelParameters

input parameters

get_point_lens_finite_source_magnification(u, pspl_magnification, direct=False)

Calculate magnification for point lens and finite source (for a uniform source). The approximation was proposed by:

Gould A. 1994 ApJ 421L, 71 “Proper motions of MACHOs”

and later the integral calculation was simplified by:

Yoo J. et al. 2004 ApJ 603, 139 “OGLE-2003-BLG-262: Finite-Source Effects from a Point-Mass Lens”

This approach assumes rho is small (rho < 0.1). For larger sources use get_point_lens_uniform_integrated_magnification().

Parameters :

u: float, np.array

The instantaneous source-lens separation. Multiple values can be provided.

pspl_magnification: float, np.array

The point source, point lens magnification at each value of u.

direct: boolean

Use direct calculation (slow) instead of interpolation.

Returns :

magnification: float, np.array

The finite source source magnification. Type is the same as of u parameter.

get_point_lens_limb_darkening_magnification(u, pspl_magnification, gamma, direct=False)

calculate magnification for point lens and finite source with limb darkening. The approximation was proposed by:

Gould A. 1994 ApJ 421L, 71 “Proper motions of MACHOs”

and later the integral calculation was simplified by:

Yoo J. et al. 2004 ApJ 603, 139 “OGLE-2003-BLG-262: Finite-Source Effects from a Point-Mass Lens”

Parameters :

u: float, np.array

The instantaneous source-lens separation. Multiple values can be provided.

pspl_magnification: float, np.array

The point source, point lens magnification at each value of u.

gamma: float

The limb-darkening coefficient. See also LimbDarkeningCoeffs

direct: boolean

Use direct calculation (very slow) instead of interpolation.

Returns :

magnification: float, np.array

The finite source source magnification including limb-darkening. Type is the same as of u parameter.

get_point_lens_uniform_integrated_magnification(u, rho)

Calculate magnification for the point lens and uniform finite source. This approach works well for small and large sources (e.g., rho~0.5). Uses the method presented by:

Lee, C.-H. et al. 2009 ApJ 695, 200 “Finite-Source Effects in Microlensing: A Precise, Easy to Implement, Fast, and Numerically Stable Formalism”

Parameters :

u: np.array

The instantaneous source-lens separation.

rho: float

Source size as a fraction of the Einstein radius.

Returns :

magnification: np.array

The finite source magnification.

get_point_lens_LD_integrated_magnification(u, rho, gamma)

Calculate magnification for the point lens and finite source with limb-darkening. This approach works well for small and large sources (e.g., rho~0.5). Uses the method presented by:

Lee, C.-H. et al. 2009 ApJ 695, 200 “Finite-Source Effects in Microlensing: A Precise, Easy to Implement, Fast, and Numerically Stable Formalism”

Parameters :

u: np.array

The instantaneous source-lens separation.

rho: float

Source size as a fraction of the Einstein radius.

gamma: float

Gamma limb darkening coefficient. See also LimbDarkeningCoeffs.

Returns :

magnification: np.array

The finite source magnification.

get_point_lens_large_finite_source_magnification(u)

Calculate magnification for the point lens and uniform source. This approach works well for small and large sources (e.g., rho~0.5). The method was presented by:

Witt and Mao 1994 ApJ 430, 505 “Can Lensed Stars Be Regarded as Pointlike for Microlensing by MACHOs?”

Parameters :

u: np.array

The instantaneous source-lens separation.

Returns :

magnification: np.array

The finite source magnification.

get_point_lens_large_LD_integrated_magnification(u, gamma)

Calculate magnification for the point lens and finite source with limb-darkening. This approach works well for small and large sources (e.g., rho~0.5). Here multiple annuli (each with uniform source) are used to approximate finite source with limb-darkening. For uniform source calculation see:

Witt and Mao 1994 ApJ 430, 505 “Can Lensed Stars Be Regarded as Pointlike for Microlensing by MACHOs?”

The approximation of multiple sources in presented by, e.g.,:

Bozza et al. 2018 MNRAS 479, 5157 “VBBINARYLENSING: a public package for microlensing light-curve computation”

Parameters :

u: np.array

The instantaneous source-lens separation.

gamma: float

Gamma limb darkening coefficient. See also LimbDarkeningCoeffs.

Returns :

magnification: np.array

The finite source magnification.