#include <EinastoGeometry.hpp>

Inheritance diagram for EinastoGeometry:

[legend]

Public Member Functions
double	density (double r) const override

double	halfMassRadius () 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
	EinastoGeometry ()

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 = EinastoGeometry

Private Attributes
double	_dn

double	_halfMassRadius

double	_index

const double &	_n

double	_rhos

const double &	_rs

Array	_rv

Array	_Xv

Friends
class	ItemRegistry

Detailed Description

The EinastoGeometry class is a subclass of the SpheGeometry class, and describes spherical geometries characterized by an Einasto density profile (Einasto 1965),

$ρ (r) = ρ_{s} \exp {- d_{n} [{(\frac{r}{r_{s}})}^{1 / n} - 1]} .$

This geometry has two free parameters: the half mass radius $r_{s}$ , and the Einasto index $n$ . The quantity $d_{n}$ is not a free parameter, but a numerical constant that guarantees that $r_{s}$ is the radius of the sphere that contains half of the total mass. A numerical approximation for $d_{n}$ is provided by Retana-Montenegro et al. (2012):

$d_{n} = 3 n + - \frac{1}{3} + \frac{8}{1215 n} + \frac{184}{229635 n^{2}} + \frac{1048}{31000725 n^{3}} .$

Constructor & Destructor Documentation

◆ EinastoGeometry()

EinastoGeometry::EinastoGeometry ( )

inlineprotected

Default constructor for concrete Item subclass EinastoGeometry : "an Einasto geometry" .

Member Function Documentation

◆ density()

double EinastoGeometry::density ( double r ) const

overridevirtual

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

Implements SpheGeometry.

◆ halfMassRadius()

EinastoGeometry::halfMassRadius ( ) const

inline

This function returns the value of the discoverable double property halfMassRadius : "the half-mass radius" .

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

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

◆ index()

EinastoGeometry::index ( ) const

inline

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

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

◆ randomRadius()

double EinastoGeometry::randomRadius ( ) const

overridevirtual

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

Implements SpheGeometry.

◆ setupSelfBefore()

void EinastoGeometry::setupSelfBefore ( )

overrideprotectedvirtual

This function calculates some frequently used values. The half-mass density $ρ_{s}$ is set by the normalization condition that the total mass is equal to one. For the Einasto model we find (see Retana-Montenegro et al. 2012)

$ρ_{s} = \frac{d_{n}^{3 n}}{4 π e^{d_{n}} n Γ (3 n) r_{s}^{3}} .$

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 Einasto model,

$M (r) = P [3 n, d_{n} {(\frac{r}{r_{s}})}^{1 / n}]$

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

Reimplemented from SimulationItem.

◆ Sigmar()

double EinastoGeometry::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 Einasto geometry, one obtains

$Σ_{r} = n G a m m a (n) ρ_{s} r_{s} \frac{e^{d_{n}}}{d_{n}^{n}} .$

Implements SpheGeometry.

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

EinastoGeometry.hpp

Public Member Functions

Protected Member Functions

Private Types

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ EinastoGeometry()

Member Function Documentation

◆ density()

◆ halfMassRadius()

◆ index()

◆ randomRadius()

◆ setupSelfBefore()

◆ Sigmar()