MultiGaussianExpansionGeometry Class Reference

#include <MultiGaussianExpansionGeometry.hpp>

Inheritance diagram for MultiGaussianExpansionGeometry:

Public Member Functions
double	density (double R, double z) const override
string	filename () const
Position	generatePosition () const override
double	inclination () const
double	pixelscale () const
double	SigmaR () const override
double	SigmaZ () const override
Public Member Functions inherited from AxGeometry
virtual double	density (double R, double z) const =0
double	density (Position bfr) const override
int	dimension () const override
virtual double	SigmaR () const =0
double	SigmaX () const override
double	SigmaY () 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
	MultiGaussianExpansionGeometry ()
void	setupSelfBefore () override
Protected Member Functions inherited from AxGeometry
	AxGeometry ()
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 = AxGeometry
using	ItemType = MultiGaussianExpansionGeometry

Private Attributes
string	_filename
double	_inclination
Array	_Mcumv
Array	_Mv
int	_Ncomp
double	_pixelscale
Array	_qv
Array	_sigmav

Friends
class	ItemRegistry

Detailed Description

The MultiGaussianExpansionGeometry class is a subclass of the AxGeometry class, and describes axisymmetric geometries characterized by a combination of gaussian distributions in the radial and the vertical direction,

$$\rho (R,z)=\sum _j{\rho }_{j,0}\exp (-\frac{R^2}{2{\sigma }_j^2}-\frac{z^2}{2q_j^2{\sigma }_j^2})$$

Using a multi-gaussian expansion (MGE), one can reconstruct a large variety of geometries; see for example Emsellem, Monnet & Bacon (1994, A&A, 285, 723), Emsellem et al. (1994, A&A, 285, 739) and Cappellari (2002, MNRAS, 333, 400).

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

MultiGaussianExpansionGeometry()

MultiGaussianExpansionGeometry::MultiGaussianExpansionGeometry ( )

inlineprotected

Default constructor for concrete Item subclass MultiGaussianExpansionGeometry : "a multi-gaussian expansion geometry" .

Member Function Documentation

density()

double MultiGaussianExpansionGeometry::density ( double  R, double  z  ) const

overridevirtual

This function returns the density $\rho (R,z)$ at the cylindrical radius $R$ and height $z$. It just sums the contribution of the different MGE components.

Implements AxGeometry.

filename()

string MultiGaussianExpansionGeometry::filename ( ) const

inline

This function returns the value of the discoverable string property filename : "the name of the file with the multi-gaussian expansion parameters" .

generatePosition()

Position MultiGaussianExpansionGeometry::generatePosition ( ) const

overridevirtual

This pure virtual function generates a random position from the geometry, by drawing a random point from the three-dimensional probability density $p(\mathbf{r})\text{d}\mathbf{r}=\rho (\mathbf{r})\text{d}\mathbf{r}$. In the case of an MGE geometry, first a random component is chosen according to the discrete probability distribution $p_j=M_j$. Once this component is selected, a random position $\mathbf{r}=(x,y,z)$ is generated by choosing three random numbers $(X_1,X_2,X_3)$ from a gaussian distribution and setting

$$\begin{array}{rl}x& ={\sigma }_j{X}_1\\ y& ={\sigma }_j{X}_2\\ z& =q_j{\sigma }_j{X}_3\end{array}$$

Implements Geometry.

inclination()

MultiGaussianExpansionGeometry::inclination ( ) const

inline

This function returns the value of the discoverable double property inclination : "the inclination of the system" .

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

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

The maximum value for this property is "90 deg]" .

pixelscale()

MultiGaussianExpansionGeometry::pixelscale ( ) const

inline

This function returns the value of the discoverable double property pixelscale : "the scale of the multi-gaussian-expanded image (length per pixel)" .

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

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

setupSelfBefore()

void MultiGaussianExpansionGeometry::setupSelfBefore ( )

overrideprotectedvirtual

This function reads a file with the parameters obtained by performing a multi-gaussian expansion of an image on the sky. The file should contain three columns, with the first column the total count $N_j$ of the $j$'th component, the second column the scalelength ${\sigma }_j$ in pixel units and the third column the apparent flattening $q_j^{\prime }$ on the plane of the sky. Apart from this file, the function needs the physical pixel scale (e.g. in pc/pix) of the images that have been used for the MGE decomposition and the inclination of the system. From these data, the function calculates for each of the components the normalized mass contribution

$$M_j=\frac{N_j}{\sum _{j^{\prime }}{N}_{j^{\prime }}},$$

the scalelength ${\sigma }_j$ in physical units and the actual flattening $q_j$ of each of the components. In particular, the actual flattening is calculated from the apparent flattening and inclination of the system using the relation

$$q_j=\frac{\sqrt{{q^{\prime }}_j^2-{\cos }^{2}i}}{\sin i}$$

Reimplemented from Geometry.

SigmaR()

double MultiGaussianExpansionGeometry::SigmaR ( ) const

overridevirtual

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

$${\mathrm{\Sigma }}_R={\int }_0\mathrm{\infty }\rho (R,0)\text{d}R.$$

For the MGE geometry we find

$${\mathrm{\Sigma }}_R=\sum _j{\rho }_{0,j}{\int }_0^{\mathrm{\infty }}\exp (-\frac{R^2}{2{\sigma }_j^2})\text{d}R=\frac{1}{4\pi }\sum _j\frac{M_j}{q_j{\sigma }_j^2}.$$

Implements AxGeometry.

SigmaZ()

double MultiGaussianExpansionGeometry::SigmaZ ( ) const

overridevirtual

This function returns the Z-axis surface density, i.e. the integration of the density along the entire Z-axis,

$${\mathrm{\Sigma }}_Z={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\rho (0,0,z)\text{d}z.$$

For the MGE geometry we find

$${\mathrm{\Sigma }}_Z=\sum _j{\rho }_{0,j}{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\exp (-\frac{z^2}{2q_j^2{\sigma }_j^2})\text{d}z=\frac{1}{2\pi }\sum _j\frac{M_j}{{\sigma }_j^2}.$$

Implements Geometry.

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

• MultiGaussianExpansionGeometry.hpp