GRALE: grale::EllipticLens Class Reference

Base class for the lens effect by an elliptical lens, based on the information of the circular equivalent. More...

#include <ellipticlens.h>

Inheritance diagram for grale::EllipticLens:

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Collaboration diagram for grale::EllipticLens:

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List of all members.

Additional Inherited Members
Public Types inherited from grale::GravitationalLens
enum	LensType { Gaussian, MultiplePlummers, Plummer, Pointmass, SIS, NSIE, NSIS, SIE, Square, MultipleSquares, MultipleGaussians, MassSheet, Composite, MassDisk, Profile, PolynomialMassProfile, MultipleWendland, DeflectionGrid, NFW, EllipticNFW, Sersic, EllipticSersic }
	Specific lens types. More...
Public Member Functions inherited from grale::GravitationalLens
LensType	getLensType () const
	Returns the type of the lens.
virtual bool	init (double D_d, const GravitationalLensParams *pLensParams=0)
	Initializes the lens with parameters `params`, setting its angular diameter distance to `D_d`.
bool	traceTheta (double D_s, double D_ds, Vector2D< double > theta, Vector2D< double > *pBeta) const
	Calculates the result of the lens equation.
virtual double	getInverseMagnification (double D_s, double D_ds, Vector2D< double > theta) const
	Returns the inverse magnification factor for a specific direction.
double	getLensDistance () const
	Returns the D_d parameter used in the GravitationalLens::init function.
void	setLensDistance (double D_d)
	Changes the lens distance.
const GravitationalLensParams *	getLensParameters () const
	Returns a pointer to a copy of the lens parameters used in the GravitationalLens::init function.
virtual void	setDerivativeAngularDistanceScale (double distanceScale)
	Sets a distance scale to be used when estimating the derivatives of the function beta(theta) numerically.
bool	write (serut::SerializationInterface &si) const
	Writes the current lens to a serut::SerializationInterface instance.
bool	save (const std::string &fileName) const
	Writes the current lens to a file.
GravitationalLens *	createCopy () const
	Creates a copy of the current lens instance.
Static Public Member Functions inherited from grale::GravitationalLens
static double	getInverseMagnification (double D_s, double D_ds, double axx, double ayy, double axy)
	Calculate inverse magnification from derivatives of deflection angle.
static void	getShearInfo (double D_s, double D_ds, double axx, double ayy, double axy, double pShearAngle, double pShearSize)
	Calculate shear size and angle from derivatives of the deflection angle.
static void	getShearInfo (double gamma1, double gamma2, double pShearAngle, double pShearSize)
	Calculate shear size and angle from shear components.
static bool	read (serut::SerializationInterface &si, GravitationalLens **pLens, std::string &errorString)
	Reads a lens instance from a serut::SerializationInterface object and stores the lens in `lens`; an error message is stored in `errstr` if the function is not successful.
static bool	load (const std::string &fileName, GravitationalLens **pLens, std::string &errorString)
	Loads a lens instance from a file and stores the lens in `lens`.
Protected Member Functions inherited from grale::GravitationalLens
	GravitationalLens (LensType t)
	Meant to be used by a specific lens implementation.
virtual bool	processParameters (const GravitationalLensParams *params)=0
	Specific lens implementations implement this function to process the parameters specified in the GravitationalLens::init function.

Detailed Description

Base class for the lens effect by an elliptical lens, based on the information of the circular equivalent.

Suppose we have a circularly symmetric lens, in which the integrated (projected) mass is described by:

$\textrm{M}_c(\theta) = 2\pi D_d^2 \int_0^\theta \Sigma_c(\theta') \theta' d\theta'$

The lens effect by the mass distribution

$\Sigma\left(\vec{\theta}\right) = \Sigma_c\left(\sqrt{\theta_x^2+\frac{\theta_y^2}{q^2}}\right)$

can then be described as follows.

First, define the following quantities:

$\xi(u,x,y) = \sqrt{u\left(x^2+\frac{y^2}{1-(1-q^2)u}\right)}$

$\textrm{H}(\theta) = \frac{1}{\theta}\frac{d\Sigma_c}{d\theta}(\theta)$

$\textrm{I}(x,y) = \frac{4 G}{c^2 D_d}\int_0^1 \frac{\textrm{M}_c\left(\xi(u,x,y)\right)}{u} \frac{1}{\sqrt{1-(1-q^2)u}} du$

$\textrm{J}_n(x,y) = \frac{4 \pi G D_d}{c^2} \int_0^1 \frac{\Sigma_c\left(\xi(u,x,y)\right)}{\left(1-(1-q^2)u\right)^{\left(n+\frac{1}{2}\right)}} du$

$\textrm{K}_n(x,y) = \frac{4 \pi G D_d}{c^2} \int_0^1 \textrm{H}\left(\xi(u,x,y)\right) \frac{u}{\left(1-(1-q^2)u\right)^{\left(n+\frac{1}{2}\right)}} du$

One then has the following expressions for the lensing potential, deflection angle and its derivatives:

$\psi\left(\vec{\theta}\right) = \frac{D_{ds}}{D_s} \frac{q}{2} \textrm{I}(\theta_x, \theta_y)$

$\hat{\alpha}_x\left(\vec{\theta}\right) = q \theta_x \textrm{J}_0(\theta_x, \theta_y)$

$\hat{\alpha}_y\left(\vec{\theta}\right) = q \theta_y \textrm{J}_1(\theta_x, \theta_y)$

$\frac{\partial \hat{\alpha}_x}{\partial\theta_x}\left(\vec{\theta}\right) = q \textrm{J}_0(\theta_x, \theta_y) + q \theta_x^2 \textrm{K}_0(\theta_x, \theta_y)$

$\frac{\partial \hat{\alpha}_y}{\partial\theta_y}\left(\vec{\theta}\right) = q \textrm{J}_1(\theta_x, \theta_y) + q \theta_y^2 \textrm{K}_2(\theta_x, \theta_y)$

$\frac{\partial \hat{\alpha}_x}{\partial\theta_y}\left(\vec{\theta}\right) = q \theta_x\theta_y \textrm{K}_1(\theta_x, \theta_y)$

References

Keeton, C., A Catalog of Mass Models for Gravitational Lensing, arXiv:astro-ph/0102341, February 2001.

The documentation for this class was generated from the following file:

src/lens/ellipticlens.h

Additional Inherited Members

Detailed Description