Extended source

caustics.extended_source

Compute the magnification of an extended source using contour integration.

mag_extended_source(w0, rho, nlenses = 2, npts_limb = 150, limb_darkening = False, u1 = 0.0, npts_ld = 100, roots_itmax = 2500, roots_compensated = False, **params)

Compute the magnification of an extended source with radius rho for a system with nlenses lenses. If nlenses is 2 (binary lens) or 3 (triple lens), the coordinate system is set up such that the the origin is at the center of mass of the first two lenses which are both located on the real line. The location of the first lens is \(-sq/(1 + q)\) and the second lens is at \(s/(1 + q)\). The optional third lens is located at an arbitrary position in the complex plane \(r_3e^{-i*\psi}\). The magnification is computed using contour integration in the image plane. Boolean flag limb_darkening indicated whether linear limb-darkening needs to taken into account. If limb_darkening is set to True the linear limb-darkening coefficient u1 needs to be specified as well.

If nlenses is 2 only the parameters s and q should be specified. If nlenses is 3, the parameters s, q, q3, r3 and psi should be specified.

Note

Turning on limb-darkening (limb_darkening=True) slows down the computation by up to an order of magnitude.

Parameters:

Name	Type	Description	Default
w0	complex	Source position in the complex plane.	required
rho	float	Source radius in Einstein radii.	required
nlenses	int	Number of lenses in the system.	2
npts_limb	int	Initial number of points uniformly distributed on the source limb when computing the point source magnification. The final number of points is greater than this value because the number of points is decreased geometrically by a factor of 1/2 until it reaches 2.	150
limb_darkening	bool	If True, compute the magnification of a limb-darkened source. If limb_darkening is enabled the u1 linear limb-darkening coefficient needs to be specified. Defaults to False.	False
u1	float	Linear limb darkening coefficient. Defaults to 0..	0.0
npts_ld	int	Number of points at which the stellar brightness function is evaluated when computing contour integrals \(\int P(z_1^\prime, z_2) dz_1^\prime\) and \(\int Q(z_1, z_2^\prime) dz_2^\prime\) (see Dominik 1998). Defaults to 100.	100
s	float	Separation between the two lenses. The first lens is located at \(-sq/(1 + q)\) and the second lens is at \(s/(1 + q)\) on the real line.	required
q	float	Mass ratio defined as \(m_2/m_1\).	required
q3	float	Mass ratio defined as \(m_3/m_1\).	required
r3	float	Magnitude of the complex position of the third lens.	required
psi	float	Phase angle of the complex position of the third lens.	required
roots_itmax	int	Number of iterations for the root solver.	2500
roots_compensated	bool	Whether to use the compensated arithmetic version of the Ehrlich-Aberth root solver.	False

Returns:

Name	Type	Description
float		Total magnification at the source position w0.