Ferrers density profile (with finite size R and density (1-(r/R)^2)^2). More...

#include <potential.h>

Inheritance diagram for smile::CPotentialFerrers:

Collaboration diagram for smile::CPotentialFerrers:

Public Member Functions
	CPotentialFerrers (double _mass, double _R, double _q, double _p)

virtual CPotential *	clone () const
	Return a pointer to a copy of this instance of potential. More...

virtual POTENTIALTYPE	PotentialType () const
	enumerable potential type

virtual const char *	PotentialName () const
	string representation of potential type

virtual SYMMETRYTYPE	symmetry () const
	returns symmetry type of this potential

virtual double	Rho (double X, double Y, double Z, double t=0) const
	returns density at given coordinates, this should obviously be overriden in derivative classes

virtual double	Phi (double X, double Y, double Z, double t=0) const
	Return potential at a given spatial point (possibly a time-varying one). More...

virtual void	Force (const double xyz[N_DIM], const double t, double force, double forceDeriv=NULL) const
	Compute forces and, optionally, force derivatives at a given point. More...

virtual double	getGamma () const
	returns inner density slope estimate (only used in BSE potential expansion for the automatic selection of shape parameter Alpha)

Public Member Functions inherited from smile::CDensity
virtual double	Mass (const double r) const
	returns mass inside given radius (approximately! not necessary to integrate density over sphere, just a rough estimate used e.g. in choosing radial nodes of Schwarzschild grid)

virtual double	totalMass () const
	returns estimated M(r=infinity) or -1 if mass is infinite

double	getRadiusByMass (const double m) const
	solves for Mass(r)=m

void	getRadiiByMass (const vectord &masses, vectord *radii) const
	solves for Mass(r)=m for an array of sorted values of m (more efficient than doing it one-by-one)

bool	checkMassMonotonic () const
	safety measure: check (roughly) that mass is increasing with radius

bool	checkDensityNonzero () const
	another safety measure: check that density doesn't drop to zero along any of three axes (important to assess spherical-harmonic approximation quality)

Static Public Member Functions
static const char *	myName ()

Private Member Functions
void	computeW (double lambda, double W[20]) const
	compute the array of 20 coefficients W_{ijk} listed in Pfenniger(1984), in order of appearance in that paper; More...

Private Attributes
const double	a

const double	b

const double	c
	principal axis of ellipsoidal density

const double	mass

const double	rho0
	total mass and central density of the model

double	W0 [20]
	pre-computed coefficients for lambda=0

Additional Inherited Members
Public Types inherited from smile::CDensity
enum	POTENTIALTYPE { PT_UNKNOWN, PT_DIRECT, PT_COMPOSITE, PT_COEFS, PT_NB, PT_BSE, PT_BSECOMPACT, PT_SPLINE, PT_CYLSPLINE, PT_LOG, PT_HARMONIC, PT_SCALEFREE, PT_SCALEFREESH, PT_SPHERICAL, PT_DEHNEN, PT_MIYAMOTONAGAI, PT_FERRERS, PT_PLUMMER, PT_ISOCHRONE, PT_PERFECTELLIPSOID, PT_NFW, PT_SERSIC, PT_EXPDISK, PT_ELLIPSOIDAL, PT_MGE }
	list of all existing types of density or density/potential models, each of them implemented in its own class More...

enum	SYMMETRYTYPE { ST_NONE = 0, ST_REFLECTION = 1, ST_PLANESYM = 2, ST_ZROTSYM = 4, ST_SPHSYM = 8, ST_TRIAXIAL = ST_REFLECTION \| ST_PLANESYM, ST_AXISYMMETRIC = ST_TRIAXIAL \| ST_ZROTSYM, ST_SPHERICAL = ST_AXISYMMETRIC \| ST_SPHSYM, ST_DEFAULT = ST_TRIAXIAL }
	Type of symmetry. More...

Detailed Description

Ferrers density profile (with finite size R and density (1-(r/R)^2)^2).

The potential is calculated using expressions from Pfenniger(1984) with elliptic integrals, under assumption that p<q<1 strictly (will not work if any of two axes are equal).

Member Function Documentation

virtual CPotential* smile::CPotentialFerrers::clone ( ) const

inlinevirtual

Return a pointer to a copy of this instance of potential.

A standard copy constructor or assignment is disabled because of different amount of data needed to be copied in different derived classes).

Implements smile::CPotential.

void smile::CPotentialFerrers::computeW	(	double	lambda,
		double	W[20]
	)		const

private

compute the array of 20 coefficients W_{ijk} listed in Pfenniger(1984), in order of appearance in that paper;

Parameters

[in]	lambda	is zero inside the model and >0 outside;
[out]	W	is the array of 20 coefs

void smile::CPotentialFerrers::Force	(	const double	xyz[N_DIM],
		const double	t,
		double *	force,
		double *	forceDeriv = `NULL`
	)		const

virtual

Compute forces and, optionally, force derivatives at a given point.

Parameters

[in]	xyz	- coordinates of the point to compute forces (array of 3 numbers)
[in]	t	- time to compute forces (matters only if potential is time-dependent)
[out]	force	- computed values of -d Phi/d x_i; output array must exist and contain N_DIM values.
[out]	forceDeriv	- if not NULL, then also compute the second derivatives of potential (which is a symmetric matrix of size N_DIM^2, thus the array must be of size N_DIM*(N_DIM+1)/2 ): first 3 values contain $-d^2 \Phi/d x_i^2$ , second three contain mixed derivatives $-d^2 \Phi/d x_1 d x_2, -d^2 \Phi/d x_2 d x_3, -d^2 \Phi/d x_3 d x_1$ .

Implements smile::CPotential.

double smile::CPotentialFerrers::Phi	(	double	X,
		double	Y,
		double	Z,
		double	t = `0`
	)		const

virtual

Return potential at a given spatial point (possibly a time-varying one).

Implements smile::CPotential.

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

potential.h
potential.cpp

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation