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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 <RingGeometry.hpp>
Public Member Functions | |
| double | density (double R, double z) const override |
| double | height () const |
| double | randomCylRadius () const override |
| double | randomZ () const override |
| double | ringRadius () const |
| double | SigmaR () const override |
| double | SigmaZ () const override |
| double | width () const |
| Public Member Functions inherited from SepAxGeometry | |
| Position | generatePosition () const override |
| Public Member Functions inherited from AxGeometry | |
| double | density (Position bfr) const override |
| int | dimension () const override |
| double | SigmaX () const override |
| double | SigmaY () 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 | |
| RingGeometry () | |
| void | setupSelfBefore () override |
| Protected Member Functions inherited from SepAxGeometry | |
| SepAxGeometry () | |
| Protected Member Functions inherited from AxGeometry | |
| AxGeometry () | |
| 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 | _A |
| double | _height |
| const double & | _hz |
| const double & | _R0 |
| double | _ringRadius |
| Array | _Rv |
| const double & | _w |
| double | _width |
| Array | _Xv |
Friends | |
| class | ItemRegistry |
The RingGeometry class is a subclass of the SepAxGeometry class and describes the geometry of a ring as one would consider in dust-lane early-type galaxies. The geometry is characterized by a gaussian profile in the radial direction and an exponential fall-off in the vertical direction, resulting in the axisymmetric density profile
\[ \rho(R,z) = A\, \exp\left[ -\frac{(R-R_0)^2}{2w^2} \right] \exp\left( -\frac{|z|}{h_z} \right). \]
There are three free parameters in this class: the radius \(R_0\) of the ring, the radial dispersion \(w\) of the ring and the vertical scale height \(h_z\).
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inlineprotected |
Default constructor for concrete Item subclass RingGeometry: "a ring geometry".
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overridevirtual |
This function returns the density \(\rho(R,z)\) at the cylindrical radius \(R\) and height \(z\). It just implements the analytical formula.
Implements AxGeometry.
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inline |
This function returns the value of the discoverable double property height: "the scale height of the ring".
This property represents a physical quantity of type "length".
The minimum value for this property is "]0".
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overridevirtual |
This function returns the cylindrical radius \(R\) of a random position drawn from the geometry, by picking a uniform deviate \({\cal{X}}\) and solving the equation
\[ {\cal{X}} = 2\pi \int_0^R \rho_R(R')\, R'\, {\text{d}}R' \]
for \(R\). We just use the vector of cumulative masses stored internally.
Implements SepAxGeometry.
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overridevirtual |
This function returns the height \(z\) of a random position drawn from the geometry, by picking a uniform deviate \({\cal{X}}\) and solving the equation
\[ {\cal{X}} = \int_{-\infty}^z \rho_z(z')\, {\text{d}}z' \]
for \(z\). For the ring geometry with its exponential vertical profile, this integration is simple, and the inversion results in
\[ z = \begin{cases} \; h_z\,\ln(2{\cal{X}}) & \text{if $0<{\cal{X}}<\tfrac{1}{2}$,} \\ \;-h_z\,\ln[2(1-{\cal{X}})] & \text{if $\tfrac{1}{2}<{\cal{X}}<1$.} \end{cases} \]
Implements SepAxGeometry.
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inline |
This function returns the value of the discoverable double property ringRadius: "the radius of the ring".
This property represents a physical quantity of type "length".
The minimum value for this property is "]0".
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overrideprotectedvirtual |
This function verifies the validity of the parameters of the geometry. The density normalization parameter \(A\) is set by the normalization condition that the total mass equals one. We find
\[ A = \frac{1}{4\pi\,w^2\,h_z \left[ {\text{e}}^{-t^2} + \sqrt{\pi}\,t\,(1 + {\text{erf}}\,t) \right]}, \]
with \(t = R_0/\sqrt{2}w\). The routine also creates a vector with the cumulative distribution \(X(r)\) corresponding to the radial part of the density, i.e. mass
\[ X(R) = \int_0^R \rho_R(R')\, R'\, {\text{d}}R' \]
at a large number of radii. For the ring geometry,
\[ \rho_R(R') = 4\pi\,A\,h_z \exp\left[ -\frac{(R-R_0)^2}{2w^2} \right], \]
and thus
\[ X(R) = 4\pi\,A\,w^2\,h_z \left[ \left({\text{e}}^{-t^2}-{\text{e}}^{-u^2}\right) + \sqrt{\pi}\,t\,({\text{erf}}\,t - {\text{erf}}\,u) \right], \]
with \(t\) as defined before and \(u = (R_0-R)/\sqrt{2}w\).
Reimplemented from Geometry.
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overridevirtual |
This function returns the surface density along a line in the equatorial plane starting at the centre of the coordinate system, i.e.
\[ \Sigma_R = \int_0^infty \rho(R,0)\,{\text{d}}R. \]
For the ring geometry we obtain
\[ \Sigma_R = \sqrt{\frac{\pi}{2}}\,A\,w \left[ 1 + {\text{erf}} \left( \frac{R_0}{\sqrt{2} w} \right) \right]. \]
Implements AxGeometry.
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overridevirtual |
This function returns the surface density along the Z-axis, i.e. the integration of the density along the entire Z-axis,
\[\Sigma_Z = \int_{-\infty}^\infty \rho(0,0,z)\, {\text{d}}z.\]
For the ring geometry we find
\[ \Sigma_{\text{f}} = 2A\,h_z\, \exp\left(-\frac{R_0^2}{2w^2}\right). \]
Implements Geometry.
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inline |
This function returns the value of the discoverable double property width: "the radial width of the ring".
This property represents a physical quantity of type "length".
The minimum value for this property is "]0".