#include <PseudoSersicGeometry.hpp>

Inheritance diagram for PseudoSersicGeometry:

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Public Member Functions
double	density (double r) const override

double	effectiveRadius () const

double	index () const

double	randomRadius () const override

double	Sigmar () const override

Public Member Functions inherited from SpheGeometry
virtual double	density (double r) const =0

double	density (Position bfr) const override

int	dimension () const override

Position	generatePosition () const override

virtual double	randomRadius () const =0

virtual double	Sigmar () const =0

double	SigmaX () const override

double	SigmaY () const override

double	SigmaZ () const override

virtual double	density (Position bfr) const =0

virtual int	dimension () const =0

virtual Position	generatePosition () const =0

virtual double	SigmaX () const =0

virtual double	SigmaY () const =0

virtual double	SigmaZ () const =0

Public Member Functions inherited from SimulationItem
template<class T >
T *	find (bool setup=true) const

template<class T >
T *	interface (int levels=-999999, bool setup=true) const

virtual string	itemName () const

void	setup ()

string	typeAndName () const

Public Member Functions inherited from Item
	Item (const Item &)=delete

virtual	~Item ()

void	addChild (Item *child)

const vector< Item * > &	children () const

virtual void	clearItemListProperty (const PropertyDef *property)

void	destroyChild (Item *child)

virtual bool	getBoolProperty (const PropertyDef *property) const

virtual vector< double >	getDoubleListProperty (const PropertyDef *property) const

virtual double	getDoubleProperty (const PropertyDef *property) const

virtual string	getEnumProperty (const PropertyDef *property) const

virtual int	getIntProperty (const PropertyDef *property) const

virtual vector< Item * >	getItemListProperty (const PropertyDef *property) const

virtual Item *	getItemProperty (const PropertyDef *property) const

virtual string	getStringProperty (const PropertyDef *property) const

int	getUtilityProperty (string name) const

virtual void	insertIntoItemListProperty (const PropertyDef property, int index, Item item)

Item &	operator= (const Item &)=delete

Item *	parent () const

virtual void	removeFromItemListProperty (const PropertyDef *property, int index)

virtual void	setBoolProperty (const PropertyDef *property, bool value)

virtual void	setDoubleListProperty (const PropertyDef *property, vector< double > value)

virtual void	setDoubleProperty (const PropertyDef *property, double value)

virtual void	setEnumProperty (const PropertyDef *property, string value)

virtual void	setIntProperty (const PropertyDef *property, int value)

virtual void	setItemProperty (const PropertyDef property, Item item)

virtual void	setStringProperty (const PropertyDef *property, string value)

void	setUtilityProperty (string name, int value)

virtual string	type () const

Protected Member Functions
	PseudoSersicGeometry ()

void	setupSelfBefore () override

Protected Member Functions inherited from SpheGeometry
	SpheGeometry ()

Protected Member Functions inherited from Geometry
	Geometry ()

Random *	random () const

void	setupSelfBefore () override

Protected Member Functions inherited from SimulationItem
	SimulationItem ()

virtual bool	offersInterface (const std::type_info &interfaceTypeInfo) const

virtual void	setupSelfAfter ()

virtual void	setupSelfBefore ()

Protected Member Functions inherited from Item
	Item ()

Private Types
using	BaseType = SpheGeometry

using	ItemType = PseudoSersicGeometry

Private Attributes
double	_bn

double	_effectiveRadius

double	_index

const double &	_n

const double &	_reff

double	_rhon

Array	_rv

Array	_Xv

Friends
class	ItemRegistry

Detailed Description

The PseudoSersicGeometry class is a subclass of the SpheGeometry class, and describes geometries that are a very good approximation of a Sersic density profile. This geometry, introduced by Prugniel & Simien (1997, A&A, 321,111) is an approximation of the Sersic geometry and has the advantage that the space density is known analytically rather than the density projected on the sky. The pseudo-Sersic geometry is characterized by the density profile,

$ρ (r) = ρ_{n} {(\frac{r}{r_{eff}})}^{\frac{1}{2 n} - 1} \exp [- b_{n} {(\frac{r}{r_{eff}})}^{\frac{1}{n}}] .$

The parameter $b_{n}$ is a dimensionless number given by

$b_{n} = 2 n - \frac{1}{3} + \frac{4}{405 n} + \frac{46}{25515 n^{2}} + \frac{131}{1148175 n^{3}} .$

The geometry has two free parameters: the Sersic index $n$ and the effective radius $r_{eff}$ .

This item type is displayed only if the Boolean expression "Level2" evaluates to true after replacing the names by true or false depending on their presence.

Constructor & Destructor Documentation

◆ PseudoSersicGeometry()

PseudoSersicGeometry::PseudoSersicGeometry ( )

inlineprotected

Default constructor for concrete Item subclass PseudoSersicGeometry : "a pseudo-Sérsic geometry" .

Member Function Documentation

◆ density()

double PseudoSersicGeometry::density ( double r ) const

overridevirtual

This function returns the density $ρ (r)$ at the radius $r$ . It just implements the analytical formula.

Implements SpheGeometry.

◆ effectiveRadius()

PseudoSersicGeometry::effectiveRadius ( ) const

inline

This function returns the value of the discoverable double property effectiveRadius : "the effective radius" .

This property represents a physical quantity of type "length" .

The minimum value for this property is "]0" .

◆ index()

PseudoSersicGeometry::index ( ) const

inline

This function returns the value of the discoverable double property index : "the Sérsic index n" .

The minimum value for this property is "]0.5" .

The maximum value for this property is "10]" .

The default value for this property is given by the conditional value expression "1" .

◆ randomRadius()

double PseudoSersicGeometry::randomRadius ( ) const

overridevirtual

This function returns the radius of a random position drawn from the pseudo-Sersic geometry. We just use the vector of cumulative masses stored internally.

Implements SpheGeometry.

◆ setupSelfBefore()

void PseudoSersicGeometry::setupSelfBefore ( )

overrideprotectedvirtual

This function calculates some frequently used values. The density scale $ρ_{n}$ is set by the normalization condition that the total mass is equal to one. We easily find that

$ρ_{n} = \frac{b_{n}^{2 n + \frac{1}{2}}}{4 π r_{eff}^{3} n Γ (2 n + \frac{1}{2})} .$

We also set of a vector with the cumulative mass

$M (r) = 4 π \int_{0}^{r} ρ (r^{'}) r^{' 2} d r^{'}$

at a large number of radii. For the pseudo-Sersic model,

$M (r) = P [\frac{1}{2} + 2 n, b_{n} {(\frac{r}{r_{e}})}^{1 / n}]$

where $P (a, x)$ is the incomplete Gamma function.

Reimplemented from Geometry.

◆ Sigmar()

double PseudoSersicGeometry::Sigmar ( ) const

overridevirtual

This function returns the radial surface density, i.e. the integration of the density along a line starting at the centre of the coordinate system,

$Σ_{r} = \int_{0}^{\infty} ρ (r) d r .$

For the pseudo-Sersic geometry, one finds

$Σ_{r} = \frac{\sqrt{π} n ρ_{0} r_{eff}}{\sqrt{b_{n}}} .$

Implements SpheGeometry.

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

PseudoSersicGeometry.hpp

Public Member Functions

Protected Member Functions

Private Types

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ PseudoSersicGeometry()

Member Function Documentation

◆ density()

◆ effectiveRadius()

◆ index()

◆ randomRadius()

◆ setupSelfBefore()

◆ Sigmar()