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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 <SersicGeometry.hpp>
Public Member Functions | |
| ~SersicGeometry () | |
| double | density (double r) const override |
| double | effectiveRadius () const |
| double | index () const |
| double | randomRadius () const override |
| double | Sigmar () const override |
| Public Member Functions inherited from SpheGeometry | |
| double | density (Position bfr) const override |
| int | dimension () const override |
| Position | generatePosition () const override |
| double | SigmaX () const override |
| double | SigmaY () const override |
| double | SigmaZ () 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 | |
| SersicGeometry () | |
| void | setupSelfBefore () override |
| Protected Member Functions inherited from SpheGeometry | |
| SpheGeometry () | |
| 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 Attributes | |
| double | _b |
| double | _effectiveRadius |
| double | _index |
| const double & | _n |
| const double & | _reff |
| double | _rho0 |
| SersicFunction * | _sersicfunction |
Friends | |
| class | ItemRegistry |
The SersicGeometry class is a subclass of the SpheGeometry class, and describes spherically symmetric stellar geometries characterized by the density distribution
\[ \rho(r) = \rho_0\, {\cal{S}}_n \left(\frac{r}{r_{\text{eff}}}\right), \]
with \({\cal{S}}_n(s)\) the Sersic function of order \(n\) (see SersicFunction). It is defined in such a way that the projected surface brightness profile has the form
\[ I(r_p) = I_0 \exp \left[ -b_n\left( \frac{r_p}{r_{\text{eff}}} \right)^{1/n} \right]. \]
Two parameters characterize a SersicGeometry class object: the Sersic index \(n\) and the effective radius \(r_{\text{eff}}\). Internally, the SersicGeometry class has a SersicFunction object as one of its data members. See Sersic (1963) and Ciotti & Bertin (1999, A&A 352, 447–451).
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inlineprotected |
Default constructor for concrete Item subclass SersicGeometry: "a Sérsic geometry".
| SersicGeometry::~SersicGeometry | ( | ) |
The destructor; it deallocates the sersic function object created during setup.
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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 effectiveRadius: "the effective radius".
This property represents a physical quantity of type "length".
The minimum value for this property is "]0".
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inline |
This function returns the value of the discoverable double property index: "the Sérsic index n".
The minimum value for this property is "]0.5".
The maximum value for this property is "10]".
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 Sersic density 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 Sersic model, we use the SersicFunction::inversemass() function to solve this equation.
Implements SpheGeometry.
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overrideprotectedvirtual |
This function creates a SersicFunction class object. The central density \(\rho_0\) is set by the normalization condition that the total mass is equal to one. Since the Sersic function satisfies the normalization
\[ 4\pi \int_0^\infty {\cal{S}}_n(s)\, s^2\, {\text{d}}s = 1, \]
we easily find
\[ \rho_0 = \frac{1}{r_{\text{eff}}^3} \]
This function also caches the value of the dimensionless constant \(b_n\) that appears in the definition of the Sersic profile. A suitable approximation is
\[ b_n = 2n -\frac{1}{3} + \frac{4}{405n} + \frac{46}{25515n^2} + \frac{131}{1148175n^3}. \]
Reimplemented from Geometry.
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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 Sersic geometry, one finds
\[ \Sigma_r = \frac{1}{r_{\text{eff}}^2}\, \frac{b_n^{2n}}{ 2\pi\, \Gamma(2n+1)}. \]
Implements SpheGeometry.