#include <ExpDiskGeometry.hpp>

Inheritance diagram for ExpDiskGeometry:

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Public Member Functions
double	maxRadius () const

double	maxZ () const

double	minRadius () const

double	scaleHeight () const

double	scaleLength () const

Public Member Functions inherited from SepAxGeometry
Position	generatePosition () const override

virtual double	randomCylRadius () const =0

virtual double	randomZ () const =0

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
	ExpDiskGeometry ()

double	density (double R, double z) const override

double	randomCylRadius () const override

double	randomZ () const override

void	setupSelfBefore () override

double	SigmaR () const override

double	SigmaZ () const override

Protected Member Functions inherited from SepAxGeometry
	SepAxGeometry ()

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 = SepAxGeometry

using	ItemType = ExpDiskGeometry

Private Attributes
const double &	_hR

const double &	_hz

double	_maxRadius

double	_maxZ

double	_minRadius

double	_rho0

const double &	_Rmax

const double &	_Rmin

double	_scaleHeight

double	_scaleLength

const double &	_zmax

Friends
class	ItemRegistry

Detailed Description

The ExpDiskGeometry class is a subclass of the SepAxGeometry class, and describes axisymmetric geometries characterized by a double-exponential profile, in which the density decreases exponentially in the radial and the vertical directions; see van der Kruit (1986, A&A, 157, 230–244). A truncation can be applied in both the radial and vertical direction, and an inner cylindrical hole can be included. In formula form

$ρ (R, z) = ρ_{0} e^{- \frac{R}{h_{R}} - \frac{| z |}{h_{z}}},$

for $R_{min} \leq R \leq R_{max}$ and $| z | \leq z_{max}$ . The model contains five free parameters: the scale length $h_{R}$ , the vertical scale height $h_{z}$ , the radial truncation radius $R_{max}$ , the vertical truncation radius $z_{max}$ , and the inner radius $R_{min}$ .

Constructor & Destructor Documentation

◆ ExpDiskGeometry()

ExpDiskGeometry::ExpDiskGeometry ( )

inlineprotected

Default constructor for concrete Item subclass ExpDiskGeometry : "an exponential disk geometry" .

Member Function Documentation

◆ density()

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

overrideprotectedvirtual

This function returns the density $ρ (R, z)$ at the cylindrical radius $R$ and height $z$ . It just implements the analytical formula.

Implements AxGeometry.

◆ maxRadius()

ExpDiskGeometry::maxRadius ( ) const

inline

This function returns the value of the discoverable double property maxRadius : "the truncation radius (zero means no truncation)" .

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

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

The default value for this property is given by the conditional value expression "0" .

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

◆ maxZ()

ExpDiskGeometry::maxZ ( ) const

inline

This function returns the value of the discoverable double property maxZ : "the truncation height (zero means no truncation)" .

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

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

The default value for this property is given by the conditional value expression "0" .

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

◆ minRadius()

ExpDiskGeometry::minRadius ( ) const

inline

This function returns the value of the discoverable double property minRadius : "the radius of the central cavity" .

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

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

The default value for this property is given by the conditional value expression "0" .

◆ randomCylRadius()

double ExpDiskGeometry::randomCylRadius ( ) const

overrideprotectedvirtual

This function returns the cylindrical radius $R$ of a random position drawn from the geometry, by picking a uniform deviate $X$ and solving the equation

$X = 2 π \int_{0}^{R} ρ_{R} (R^{'}) R^{'} d R^{'}$

for $R$ . Substituting the exponential radial profile (without truncation) into this equation, we obtain

$X = 1 - (1 + \frac{R}{h_{R}}) \exp (- \frac{R}{h_{R}}) .$

This equation can be solved by means of the Lambert function of order $- 1$ , yielding

$R = h_{R} [- 1 - W_{- 1} (\frac{X - 1}{e})] .$

The Lambert function $W_{- 1} (z)$ is implemented in the function SpecialFunctions::LambertW1. The truncation and the inner hole are taken into account by rejecting values larger than $R_{max}$ or smaller than $R_{min}$ .

Implements SepAxGeometry.

◆ randomZ()

double ExpDiskGeometry::randomZ ( ) const

overrideprotectedvirtual

This function returns the height $z$ of a random position drawn from the geometry, by picking a uniform deviate $X$ and solving the equation

$X = \int_{- \infty}^{z} ρ_{z} (z^{'}) d z^{'}$

for $z$ . For the exponential disk geometry, this integration is simple, and the inversion results in

$z = {\begin{cases} h_{z} \ln (2 X) & if 0 < X < \frac{1}{2}, \\ - h_{z} \ln [2 (1 - X)] & if \frac{1}{2} < X < 1 . \end{cases}$

The truncation is taken into account by rejecting values $| z |$ larger than $z_{max}$ .

Implements SepAxGeometry.

◆ scaleHeight()

ExpDiskGeometry::scaleHeight ( ) const

inline

This function returns the value of the discoverable double property scaleHeight : "the scale height" .

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

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

◆ scaleLength()

ExpDiskGeometry::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 ExpDiskGeometry::setupSelfBefore ( )

overrideprotectedvirtual

This function verifies the validity of the parameters. The central density $ρ_{0}$ is set by the normalization condition that the total mass equals one. One finds after some elementary calculus

$\frac{1}{ρ_{0}} = 4 π h_{R}^{2} h_{z} (1 - e^{- z_{max} / h_{z}}) [(1 + \frac{R_{min}}{h_{R}}) e^{- R_{min} / h_{R}} - (1 + \frac{R_{max}}{h_{R}}) e^{- R_{max} / h_{R}}] .$

In case there is no truncation in either radial or vertical directions and no inner hole, this reduces to

$ρ_{0} = \frac{1}{4 π h_{R}^{2} h_{z}} .$

Reimplemented from SimulationItem.

◆ SigmaR()

double ExpDiskGeometry::SigmaR ( ) const

overrideprotectedvirtual

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

$Σ_{R} = \int_{0} \infty ρ (R, 0) d R .$

For the exponential disc geometry we find

$Σ_{R} = ρ_{0} h_{R} (e^{- R_{min} / h_{R}} - e^{- R_{max} / h_{R}}),$

which reduces to $Σ_{R} = ρ_{0} h_{R}$ if there is no radial truncation and no inner hole.

Implements AxGeometry.

◆ SigmaZ()

double ExpDiskGeometry::SigmaZ ( ) const

overrideprotectedvirtual

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

$Σ_{Z} = \int_{- \infty}^{\infty} ρ (0, 0, z) d z .$

For the exponential disc geometry we find

$Σ_{Z} = 2 ρ_{0} h_{Z} (1 - e^{- z_{max} / h_{z}}),$

which reduces to $Σ_{Z} = 2 ρ_{0} h_{z}$ if there is no vertical truncation. If there is an inner hole, obviously $Σ_{Z} = 0$ .

Implements Geometry.

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

ExpDiskGeometry.hpp

Public Member Functions

Protected Member Functions

Private Types

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ ExpDiskGeometry()

Member Function Documentation

◆ density()

◆ maxRadius()

◆ maxZ()

◆ minRadius()

◆ randomCylRadius()

◆ randomZ()

◆ scaleHeight()

◆ scaleLength()

◆ setupSelfBefore()

◆ SigmaR()

◆ SigmaZ()