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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 <GammaGeometry.hpp>
Public Member Functions | |
| double | density (double r) const override |
| double | gamma () const |
| double | randomRadius () const override |
| double | scaleLength () const |
| double | Sigmar () const override |
 Public Member Functions inherited from SpheGeometry | |
| virtual double | density (double r) const =0 |
| double | density (Position bfr) const override |
| int | dimension () const override |
| Position | generatePosition () const override |
| virtual double | randomRadius () const =0 |
| virtual double | Sigmar () const =0 |
| double | SigmaX () const override |
| double | SigmaY () const override |
| double | SigmaZ () 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 | |
| GammaGeometry () | |
| void | setupSelfBefore () override |
| Protected Member Functions inherited from SpheGeometry | |
| SpheGeometry () | |
| 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 = SpheGeometry |
| using | ItemType = GammaGeometry |
Private Attributes | |
| const double & | _b |
| double | _gamma |
| double | _rho0 |
| double | _scaleLength |
Friends | |
| class | ItemRegistry |
The GammaGeometry class is a subclass of the SpheGeometry class, and describes spherically symmetric geometries characterized by a gamma density profile,
\[ \rho(r) = \rho_0 \left( \frac{r}{b} \right)^{-\gamma} \left( 1 + \frac{r}{b} \right)^{\gamma-4}. \]
This model has two free parameters, namely the scale length \(b\) and the logarithmic cusp slope \(\gamma\), which should assume values between 0 and 3. The gamma models were introduced by Dehnen (1993, MNRAS, 265, 250) and Tremaine et al. (1994, AJ, 107, 634). Special cases are the Hernquist (1990, ApJ, 356, 359) model, corresponding to \(\gamma=1\), and the Jaffe (1983, MNRAS, 202, 995) model, corresponding to \(\gamma=2\).
Because the radial surface density \(\Sigma_r\) becomes infinite for \(\gamma\ge 1\), this geometry cannot be used to define a spatial medium distribution for \(\gamma\ge 1\).
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inlineprotected |
Default constructor for concrete Item subclass GammaGeometry : "a gamma geometry" .
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overridevirtual |
This function returns the density \(\rho(r)\) at a radius \(r\). It just implements the analytical formula.
Implements SpheGeometry.
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inline |
This function returns the value of the discoverable double property gamma : "the central density slope γ" .
The minimum value for this property is "[0" .
The maximum value for this property is "3[" .
The default value for this property is given by the conditional value expression "1" .
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overridevirtual |
This function returns the radius of a random position drawn from the gamma distribution. This is accomplished by generating a uniform deviate \({\cal{X}}\), and solving the equation
\[ {\cal{X}} = M(r) = 4\pi \int_0^r \rho(r')\, r'{}^2\, {\text{d}}r' \]
for \(r\). For the gamma models, we obtain the simple expression
\[ r = b\, \frac{ {\cal{X}}^{1/(3-\gamma)} }{ 1- {\cal{X}}^{1/(3-\gamma)} }. \]
Implements SpheGeometry.
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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" .
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overrideprotectedvirtual |
This function calculates some frequently used values. The central density \(\rho_0\) is set by the normalization condition that the total mass is equal to one. For the gamma model we find
\[ \rho_0 = \frac{3-\gamma}{4\pi b^3}.\]
Reimplemented from SimulationItem.
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overridevirtual |
This function returns the radial surface density, i.e. the integration of the density along a line starting at the centre of the coordinate system,
\[ \Sigma_r = \int_0^\infty \rho(r)\,{\text{d}}r. \]
For the gamma geometry, this integral does not converge if \(\gamma\ge 1\), otherwise it is equal to
\[ \Sigma_r = \frac{1}{2\pi\,b^2\,(1-\gamma)\,(2-\gamma)}. \]
Implements SpheGeometry.