routines for calculating the lensing properties of a non-singular isothermal ellipsoid written by R.B. Metcalf, March 18, 2009 based on the analytic solutions of Kormann et al. 1993 convention here is gamma_1 = -(Axx-Ayy)/2 and gamma_2= -Axy More...

#include "base_analens.h"
#include <complex>

Include dependency graph for nsie.cpp:

Namespaces
namespace	Utilities

Functions
void	alphaNSIE (PosType alpha, PosType const xt, PosType f, PosType bc, PosType theta)
	Deflection angle for non-singular isothermal ellipsoid in units of Einstein radii.

KappaType	kappaNSIE (PosType const *xt, PosType f, PosType bc, PosType theta)
	Convergence for non-singular isothermal ellipsoid, units $\frac{r_{einstein}}{units(x)}$ or $\frac{\sigma^2}{\Sigma_{crit}G\, units(xt) }$ .

void	gammaNSIE (KappaType gam, PosType const xt, PosType f, PosType bc, PosType theta)
	Shear for non-singular isothermal ellipsoid, units $\frac{r_{einstein}}{units(x)}$ or $\frac{\sigma^2}{\Sigma_{crit}G\, units(xt) }$ .

PosType	rmaxNSIE (PosType sigma, PosType mass, PosType f, PosType rc)
	Elliptical radius of a NonSingular Isothermal Ellipsoid.

PosType	ellipticRadiusNSIE (PosType const *x, PosType f, PosType pa)
	Elliptical radius given f and position angle of model.

KappaType	invmagNSIE (PosType x, PosType f, PosType bc, PosType theta, KappaType gam, KappaType kap)

void	Utilities::rotation (float xout, float xin, PosType theta)
	Rotates 2 dimensional point without changing input point.

void	Utilities::rotation (PosType xout, PosType const xin, PosType theta)
	Rotates 2 dimensional point without changing input point.

void	quadMomNSIE (float mass, float Rsize, float f, float rc, float theta, PosType *quad)

Detailed Description

routines for calculating the lensing properties of a non-singular isothermal ellipsoid written by R.B. Metcalf, March 18, 2009 based on the analytic solutions of Kormann et al. 1993 convention here is gamma_1 = -(Axx-Ayy)/2 and gamma_2= -Axy

Function Documentation

◆ alphaNSIE()

void alphaNSIE	(	PosType *	alpha,
		PosType const *	xt,
		PosType	f,
		PosType	bc,
		PosType	theta )

Deflection angle for non-singular isothermal ellipsoid in units of Einstein radii.

Parameters

alpha	Deflection angle in units of the Einstein radius
xt	position on the image plane in Einstein radius units
f	axis ratio of mass
bc	core size in same units as alpha
theta	position angle of ellipsoid

◆ gammaNSIE()

void gammaNSIE	(	KappaType *	gam,
		PosType const *	xt,
		PosType	f,
		PosType	bc,
		PosType	theta )

Shear for non-singular isothermal ellipsoid, units $\frac{r_{einstein}}{units(x)}$ or $\frac{\sigma^2}{\Sigma_{crit}G\, units(xt) }$ .

Parameters

gam	output shear
xt	position on the image plane in Einstein radius units
f	axis ratio of mass
bc	core size in units of Einstein radius
theta	position angle of ellipsoid

◆ kappaNSIE()

KappaType kappaNSIE	(	PosType const *	xt,
		PosType	f,
		PosType	bc,
		PosType	theta )

Convergence for non-singular isothermal ellipsoid, units $\frac{r_{einstein}}{units(x)}$ or $\frac{\sigma^2}{\Sigma_{crit}G\, units(xt) }$ .

Parameters

xt	position on the image plane in Einstein radius units
f	axis ratio of mass
bc	core size in units of Einstein radius
theta	position angle of ellipsoid

◆ quadMomNSIE()

void quadMomNSIE	(	float	mass,
		float	Rsize,
		float	f,
		float	rc,
		float	theta,
		PosType *	quad )

Quadropole moment of an elliptically truncated NSIE Units are unit[mass]*unit[Rsize]^2

Parameters

mass	total mass
Rsize	elliptical maximum radius
f	axis ratio of mass
rc	core size in same units as Rsize
theta	position angle of ellipsoid
quad	output

◆ rmaxNSIE()

PosType rmaxNSIE	(	PosType	sigma,
		PosType	mass,
		PosType	f,
		PosType	rc )

Elliptical radius of a NonSingular Isothermal Ellipsoid.

Parameters

sigma	velocity dispersion in km/s
mass	mass in Msun
f	axis ratio
rc	core radius Mpc

Namespaces

Functions

Detailed Description

Function Documentation

◆ alphaNSIE()

◆ gammaNSIE()

◆ kappaNSIE()

◆ quadMomNSIE()

◆ rmaxNSIE()