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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 <EinastoGeometry.hpp>
Public Member Functions | |
| double | density (double r) const override |
| double | halfMassRadius () 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 | |
| EinastoGeometry () | |
| 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 () |
| Protected Member Functions inherited from Item | |
| Item () | |
Private Types | |
| using | BaseType |
| using | ItemType |
Private Attributes | |
| double | _dn |
| double | _halfMassRadius |
| double | _index |
| const double & | _n |
| double | _rhos |
| const double & | _rs |
| Array | _rv |
| Array | _Xv |
Friends | |
| class | ItemRegistry |
The EinastoGeometry class is a subclass of the SpheGeometry class, and describes spherical geometries characterized by an Einasto density profile (Einasto 1965),
\[ \rho(r) = \rho_{\text{s}}\, \exp\left\{-d_n \left[ \left( \frac{r}{r_{\text{s}}}\right)^{1/n}-1\right] \right\}.\]
This geometry has two free parameters: the half mass radius \(r_{\text{s}}\), and the Einasto index \(n\). The quantity \(d_n\) is not a free parameter, but a numerical constant that guarantees that \(r_{\text{s}}\) is the radius of the sphere that contains half of the total mass. A numerical approximation for \(d_n\) is provided by Retana-Montenegro et al. (2012):
\[ d_n = 3n + -\frac13 + \frac{8}{1215\,n} + \frac{184}{229635\,n^2} + \frac{1048}{31000725\,n^3}. \]
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inlineprotected |
Default constructor for concrete Item subclass EinastoGeometry: "an Einasto geometry".
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overridevirtual |
This function returns the density \(\rho(r)\) at the 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 halfMassRadius: "the half-mass 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 Einasto index n".
The minimum value for this property is "]0".
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overridevirtual |
This function returns the radius of a random position drawn from the Einasto geometry. We just use the vector of cumulative masses stored internally.
Implements SpheGeometry.
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overrideprotectedvirtual |
This function calculates some frequently used values. The half-mass density \(\rho_{\text{s}}\) is set by the normalization condition that the total mass is equal to one. For the Einasto model we find (see Retana-Montenegro et al. 2012)
\[ \rho_{\text{s}} = \frac{d_n^{3n}}{ 4\pi\,{\text{e}}^{d_n}\, n\, \Gamma(3n)\,r_{\text{s}}^3 }. \]
We also set of a vector with the cumulative mass
\[ M(r) = 4\pi \int_0^r \rho(r')\, r'^2\, {\text{d}}r' \]
at a large number of radii. For the Einasto model,
\[ M(r) = P\left[3n,d_n\left(\frac{r}{r_{\text{s}}}\right)^{1/n}\right] \]
where \(P(a,x)\) is the incomplete Gamma function.
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 Einasto geometry, one obtains
\[ \Sigma_r = n\,Gamma(n)\, \rho_{\text{s}}\, r_{\text{s}}\, \frac{{\text{e}}^{d_n}}{d_n^n}. \]
Implements SpheGeometry.