PlummerGeometry Class Reference

#include <PlummerGeometry.hpp>

Inheritance diagram for PlummerGeometry:

Public Member Functions
double	density (double r) const override
double	randomRadius () const override
double	scaleLength () const
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
	PlummerGeometry ()
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 = PlummerGeometry

Private Attributes
const double &	_c
double	_rho0
double	_scaleLength

Friends
class	ItemRegistry

Detailed Description

The PlummerGeometry class is a subclass of the SpheGeometry class, and describes spherically symmetric geometries characterized by a Plummer density profile,

$$\rho (r)={\rho }_0{(1+\frac{r^2}{c^2})}^{-5/2}.$$

The only free parameter is the scale length $c$. See Plummer (1911, MNRAS, 71, 460–470) and Dejonghe (1987, MNRAS, 224, 13–39).

Constructor & Destructor Documentation

PlummerGeometry()

PlummerGeometry::PlummerGeometry ( )

inlineprotected

Default constructor for concrete Item subclass PlummerGeometry : "a Plummer geometry" .

Member Function Documentation

density()

double PlummerGeometry::density ( double  r ) const

overridevirtual

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

Implements SpheGeometry.

randomRadius()

double PlummerGeometry::randomRadius ( ) const

overridevirtual

This function returns the radius of a random position drawn from the Plummer density distribution. This is accomplished by generating a uniform deviate $\mathcal{X}$, and solving the equation

$$\mathcal{X}=M(r)=4\pi {\int }_0^r\rho (r^{\prime })r^{\prime }{}^2\text{d}{r}^{\prime }$$

for $r$. For the Plummer model, we obtain the simple expression

$$r=c\frac{{\mathcal{X}}^{1/3}}{\sqrt{1-{\mathcal{X}}^{2/3}}}.$$

Implements SpheGeometry.

scaleLength()

PlummerGeometry::scaleLength ( ) const

inline

This function returns the value of the discoverable double property scaleLength : "the scale length" .

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

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

setupSelfBefore()

void PlummerGeometry::setupSelfBefore ( )

overrideprotectedvirtual

This function calculates some frequently used values. The central density ${\rho }_0$ is set by the normalization condition that the total mass equals one. For the Plummer model we find

$${\rho }_0=\frac{3}{4\pi c^3}.$$

Reimplemented from Geometry.

Sigmar()

double PlummerGeometry::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,

$${\mathrm{\Sigma }}_r={\int }_0^{\mathrm{\infty }}\rho (r)\text{d}r.$$

For the Plummer geometry, one obtains

$${\mathrm{\Sigma }}_r=\frac{1}{2\pi c^2}.$$

Implements SpheGeometry.

---

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

• PlummerGeometry.hpp