SpiralStructureGeometryDecorator Class Reference

#include <SpiralStructureGeometryDecorator.hpp>

Inheritance diagram for SpiralStructureGeometryDecorator:

Public Member Functions
double	density (Position bfr) const override
Position	generatePosition () const override
AxGeometry *	geometry () const
int	index () const
int	numArms () const
double	perturbationWeight () const
double	phaseZeroPoint () const
double	pitchAngle () const
double	radiusZeroPoint () const
void	setupSelfBefore () override
double	SigmaX () const override
double	SigmaY () const override
double	SigmaZ () const override
Public Member Functions inherited from GenGeometry
int	dimension () 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
	SpiralStructureGeometryDecorator ()
Protected Member Functions inherited from GenGeometry
	GenGeometry ()
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 = GenGeometry
using	ItemType = SpiralStructureGeometryDecorator

Private Member Functions
double	perturbation (double R, double phi) const

Private Attributes
double	_c
double	_cn
AxGeometry *	_geometry
int	_index
const int &	_m
const int &	_N
int	_numArms
const double &	_p
double	_perturbationWeight
double	_phaseZeroPoint
const double &	_phi0
double	_pitchAngle
const double &	_R0
double	_radiusZeroPoint
double	_tanp
const double &	_w

Friends
class	ItemRegistry

Detailed Description

The SpiralStructureGeometryDecorator class is a geometry decorator that adds spiral structure to any axisymmetric geometry. The spiral arm perturbation (with an arbitrary weight factor) is a logarithmic spiral arm pattern, based on the formulation of Schechtman-Rook et al. (2012, ApJ, 746, 70). The decorator basically alters the uniform distribution in azimuth (by definition, the density ${\rho }_{\text{ax}}$ of the original geometry is independent of $\varphi$). In formula form, the density of the new geometry behaves as

$$\rho (R,\varphi ,z)={\rho }_{\text{ax}}(R,z)\xi (R,\varphi )$$

where $\xi (R,\varphi )$ is a perturbation given by

$$\xi (R,\varphi )=(1-w)+w{C}_N{\sin }^{2N}[\frac{m}{2}(\frac{\ln (R/R_0)}{\tan p}-(\varphi -{\varphi }_0))+\frac{\pi }{4}].$$

Apart from the reference to the original geometry that is being decorated, the model contains six parameters: the number of spiral arms $m$, the pitch angle $p$, the spiral arm radius and phase zero-points $R_0$ and ${\varphi }_0$, the spiral perturbation weight $w$, and the integer index $N>0$ that sets the arm-interarm size ratio (larger values of $N$ correspond to larger arm-interarm size ratios). The factor $C_N$ is not a free parameter, but a normalization factor that ensures that the total mass equals one,

$$C_N=\frac{\sqrt{\pi }\mathrm{\Gamma }(N+1)}{\mathrm{\Gamma }(N+\frac{1}{2})}.$$

For $N=1$ the expression for the perturbation reduces to

$$\xi (R,\varphi )=1+w\sin \left[m(\frac{\ln (R/R_0)}{\tan p}-(\varphi -{\varphi }_0))\right],$$

as in Misiriotis et al. (2000, A&A, 353, 117). Note that the parameters $R_0$ and ${\varphi }_0$ in fact have the same effect (both of them add an offset to the spiral structure). In principle one of them could be suppressed, but it is confortable to include both of them.

Constructor & Destructor Documentation

SpiralStructureGeometryDecorator()

SpiralStructureGeometryDecorator::SpiralStructureGeometryDecorator ( )

inlineprotected

Default constructor for concrete Item subclass SpiralStructureGeometryDecorator : "a decorator that adds spiral structure to any axisymmetric geometry" .

Member Function Documentation

density()

double SpiralStructureGeometryDecorator::density ( Position  bfr ) const

overridevirtual

This function returns the density $\rho (\mathbf{r})$ at the position $\mathbf{r}$. It just implements the analytical formula.

Implements Geometry.

generatePosition()

Position SpiralStructureGeometryDecorator::generatePosition ( ) const

overridevirtual

This function generates a random position from the geometry by drawing a random point from the three-dimensional probability density $p(\mathbf{r})\text{d}\mathbf{r}=\rho (\mathbf{r})\text{d}\mathbf{r}$. We use a combination of the conditional distribution technique and the rejection technique.

Implements Geometry.

geometry()

AxGeometry * SpiralStructureGeometryDecorator::geometry ( ) const

inline

This function returns the value of the discoverable item property geometry : "the axisymmetric geometry to be decorated with spiral structure" .

index()

SpiralStructureGeometryDecorator::index ( ) const

inline

This function returns the value of the discoverable integer property index : "the arm-interarm size ratio index" .

The minimum value for this property is "0" .

The maximum value for this property is "10" .

The default value for this property is given by the conditional value expression "1" .

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.

numArms()

SpiralStructureGeometryDecorator::numArms ( ) const

inline

This function returns the value of the discoverable integer property numArms : "the number of spiral arms" .

The minimum value for this property is "1" .

The maximum value for this property is "100" .

The default value for this property is given by the conditional value expression "1" .

perturbation()

double SpiralStructureGeometryDecorator::perturbation ( double  R, double  phi  ) const

private

This private function implements the analytical formula for the perturbation $\xi (R,\varphi )$.

perturbationWeight()

SpiralStructureGeometryDecorator::perturbationWeight ( ) const

inline

This function returns the value of the discoverable double property perturbationWeight : "the weight of the spiral perturbation" .

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

The maximum value for this property is "1]" .

phaseZeroPoint()

SpiralStructureGeometryDecorator::phaseZeroPoint ( ) const

inline

This function returns the value of the discoverable double property phaseZeroPoint : "the phase zero-point" .

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

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

The maximum value for this property is "360 deg]" .

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

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.

pitchAngle()

SpiralStructureGeometryDecorator::pitchAngle ( ) const

inline

This function returns the value of the discoverable double property pitchAngle : "the pitch angle" .

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

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

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

The default value for this property is given by the conditional value expression "10 deg" .

radiusZeroPoint()

SpiralStructureGeometryDecorator::radiusZeroPoint ( ) const

inline

This function returns the value of the discoverable double property radiusZeroPoint : "the radius zero-point" .

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

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

setupSelfBefore()

void SpiralStructureGeometryDecorator::setupSelfBefore ( )

overridevirtual

This function calculates some frequently used values.

Reimplemented from Geometry.

SigmaX()

double SpiralStructureGeometryDecorator::SigmaX ( ) const

overridevirtual

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

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

This integral cannot be calculated analytically, but when averaged over all lines-of-sight in the equatorial plane, the contribution of the spiral arm perturbation cancels out, and we recover the X-axis surface density of the corresponding unperturbed model.

Implements Geometry.

SigmaY()

double SpiralStructureGeometryDecorator::SigmaY ( ) const

overridevirtual

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

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

This integral cannot be calculated analytically, but when averaged over all lines-of-sight in the equatorial plane, the contribution of the spiral arm perturbation cancels out, and we recover the Y-axis surface density of the corresponding unperturbed model.

Implements Geometry.

SigmaZ()

double SpiralStructureGeometryDecorator::SigmaZ ( ) const

overridevirtual

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

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

For the present decorator, this integral is not really well defined, as the logarithmic spiral perturbation winds ever stronger when we get closer to the Z-axis. We use the Z-axis surface density of the corresponding unperturbed model.

Implements Geometry.

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

• SpiralStructureGeometryDecorator.hpp