DonutGeometry Class Reference

#include <DonutGeometry.hpp>

Inheritance diagram for DonutGeometry:

Public Member Functions
double	density (double R, double z) const override
Position	generatePosition () const override
double	largeRadius () const
double	SigmaR () const override
double	SigmaZ () const override
double	smallRadius () const
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
	DonutGeometry ()
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 = DonutGeometry

Private Attributes
double	_A
double	_largeRadius
const double &	_R0
const double &	_r0
double	_r02
double	_smallRadius

Friends
class	ItemRegistry

Detailed Description

The DonutGeometry class is a subclass of the AxGeometry class and describes the geometry of an axisymmetric ring torus (i.e. a doughnut geometry) of uniform density. This ring torus geometry is often used to model the dusty gas in the equatorial plane of active galactic nuclei (AGN), to explain the observed variety of AGN types as a distribution of observed system orientations relative to this obscuring torus of gas and dust; see Antonucci (1993, ARA&A, 31, 473), Urry & Padovani (1995, PASP, 107, 803) and Netzer (2015, ARA&A, 53, 365).

The ring torus geometry is obtained by revolving a circle of radius $r_{\text{small}}$ about an axis that is co-planar with this circle, at a radius $r_{\text{large}}$. Inside this surface of revolution the density has a constant value, and outside this surface the density is zero. In formula, this is easily expressed in cylindrical coordinates as

$$\rho (R,z)=A\text{for }\sqrt{(R-r_{\text{large}}{)}^2+z^2}<r_{\text{small}}.$$

There are two free parameters describing this torus geometry: the torus radius in the azimuthal plane $r_{\text{small}}$ and the torus radius in the equatorial plane $r_{\text{large}}$.

Constructor & Destructor Documentation

DonutGeometry()

DonutGeometry::DonutGeometry ( )

inlineprotected

Default constructor for concrete Item subclass DonutGeometry : "a donut torus geometry" .

Member Function Documentation

density()

double DonutGeometry::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 implements the geometry definition.

Implements AxGeometry.

generatePosition()

Position DonutGeometry::generatePosition ( ) const

overridevirtual

This function generates a random position from the uniform ring torus geometry. A random azimuth angle $\varphi$ is readily found by choosing a random deviate $\mathcal{X}$ and setting $\varphi =2\pi \mathcal{X}$. Then, a random position in the small circle in the azimuthal plane is found (in polar coordinates) as ${\theta }^{\prime }=2\pi {\mathcal{X}}_1$ and $r^{\prime }=r_{\text{small}}\sqrt{{\mathcal{X}}_2}$, with ${\mathcal{X}}_1$ and ${\mathcal{X}}_2$ two more random deviates. Finally, these small circle coordinates are transformed to global cylindrical coordinates as $z=r^{\prime }\sin ({\theta }^{\prime })$ and $R=r_{\text{large}}+r^{\prime }\cos ({\theta }^{\prime })$.

Implements Geometry.

largeRadius()

DonutGeometry::largeRadius ( ) const

inline

This function returns the value of the discoverable double property largeRadius : "the radius of the torus circle in the equatorial plane" .

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

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

setupSelfBefore()

void DonutGeometry::setupSelfBefore ( )

overrideprotectedvirtual

This function calculates some frequently used values. The normalization parameter $A$ is set by the normalization condition that total mass equals one, i.e.

$$A=\frac{1}{V}=\frac{1}{2{\pi }^2{r}_{\text{large}}{r}_{\text{small}}^2}.$$

Reimplemented from SimulationItem.

SigmaR()

double DonutGeometry::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 this geometry,

$${\mathrm{\Sigma }}_R=A2r_{\text{small}}.$$

Implements AxGeometry.

SigmaZ()

double DonutGeometry::SigmaZ ( ) const

overridevirtual

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

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

For this geometry, the integral is simply zero.

Implements Geometry.

smallRadius()

DonutGeometry::smallRadius ( ) const

inline

This function returns the value of the discoverable double property smallRadius : "the radius of the torus circle in the azimuthal plane" .

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

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

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

• DonutGeometry.hpp