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The SKIRT project
advanced radiative transfer for astrophysics
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The SKIRT project
advanced radiative transfer for astrophysics
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#include <SpiralStructureGeometryDecorator.hpp>
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 |
| 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 |
| Protected Member Functions inherited from SimulationItem | |
| SimulationItem () | |
| virtual bool | offersInterface (const std::type_info &interfaceTypeInfo) const |
| virtual void | setupSelfAfter () |
| Protected Member Functions inherited from Item | |
| Item () | |
Private Types | |
| using | BaseType |
| using | ItemType |
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 |
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 \(\phi\)). In formula form, the density of the new geometry behaves as
\[\rho(R,\phi,z) = \rho_{\text{ax}}(R,z)\, \xi(R,\phi) \]
where \(\xi(R,\phi)\) is a perturbation given by
\[ \xi(R,\phi) = (1-w) + w\, C_N \sin^{2N} \left[\frac{m}{2}\left( \frac{\ln (R/R_0)}{\tan p}-(\phi-\phi_0)\right) + \frac{\pi}{4} \right]. \]
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 \(\phi_0\), 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,
\[ C_N = \frac{\sqrt{\pi}\, \Gamma(N+1)}{\Gamma(N+\tfrac12)}. \]
For \(N=1\) the expression for the perturbation reduces to
\[ \xi(R,\phi) = 1 + w\, \sin \left[m \left( \frac{\ln (R/R_0)}{\tan p} - (\phi-\phi_0)\right) \right], \]
as in Misiriotis et al. (2000, A&A, 353, 117). Note that the parameters \(R_0\) and \(\phi_0\) 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.
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inlineprotected |
Default constructor for concrete Item subclass SpiralStructureGeometryDecorator: "a decorator that adds spiral structure to any axisymmetric geometry".
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overridevirtual |
This function returns the density \(\rho({\bf{r}})\) at the position \({\bf{r}}\). It just implements the analytical formula.
Implements Geometry.
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overridevirtual |
This function generates a random position from the geometry by drawing a random point from the three-dimensional probability density \(p({\bf{r}})\,{\text{d}}{\bf{r}} = \rho({\bf{r}})\, {\text{d}}{\bf{r}}\). We use a combination of the conditional distribution technique and the rejection technique.
Implements Geometry.
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inline |
This function returns the value of the discoverable item property geometry: "the axisymmetric geometry to be decorated with spiral structure".
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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.
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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".
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private |
This private function implements the analytical formula for the perturbation \(\xi(R,\phi)\).
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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]".
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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.
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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".
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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".
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overridevirtual |
This function calculates some frequently used values.
Reimplemented from Geometry.
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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,
\[\Sigma_X = \int_{-\infty}^\infty \rho(x,0,0)\, {\text{d}}x.\]
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.
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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,
\[\Sigma_Y = \int_{-\infty}^\infty \rho(0,y,0)\, {\text{d}}y.\]
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.
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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,
\[\Sigma_Z = \int_{-\infty}^\infty \rho(0,0,z)\, {\text{d}}z.\]
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.