#include <ExpDiskGeometry.hpp>
Public Member Functions | |
double | maxRadius () const |
double | maxZ () const |
double | minRadius () const |
double | scaleHeight () const |
double | scaleLength () const |
Public Member Functions inherited from SepAxGeometry | |
Position | generatePosition () const override |
virtual double | randomCylRadius () const =0 |
virtual double | randomZ () const =0 |
Public Member Functions inherited from AxGeometry | |
virtual double | density (double R, double z) const =0 |
double | density (Position bfr) const override |
int | dimension () const override |
virtual double | SigmaR () const =0 |
double | SigmaX () const override |
double | SigmaY () 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 | |
ExpDiskGeometry () | |
double | density (double R, double z) const override |
double | randomCylRadius () const override |
double | randomZ () const override |
void | setupSelfBefore () override |
double | SigmaR () const override |
double | SigmaZ () const 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 |
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 = SepAxGeometry |
using | ItemType = ExpDiskGeometry |
Friends | |
class | ItemRegistry |
The ExpDiskGeometry class is a subclass of the SepAxGeometry class, and describes axisymmetric geometries characterized by a double-exponential profile, in which the density decreases exponentially in the radial and the vertical directions; see van der Kruit (1986, A&A, 157, 230–244). A truncation can be applied in both the radial and vertical direction, and an inner cylindrical hole can be included. In formula form
\[ \rho(R,z) = \rho_0\, {\text{e}}^{-\frac{R}{h_R}-\frac{|z|}{h_z}}, \]
for \(R_{\text{min}} \leq R \leq R_{\text{max}}\) and \(|z|\leq z_{\text{max}}\). The model contains five free parameters: the scale length \(h_R\), the vertical scale height \(h_z\), the radial truncation radius \(R_{\text{max}}\), the vertical truncation radius \(z_{\text{max}}\), and the inner radius \(R_{\text{min}}\).
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inlineprotected |
Default constructor for concrete Item subclass ExpDiskGeometry : "an exponential disk geometry" .
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overrideprotectedvirtual |
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 maxRadius : "the truncation radius (zero means no truncation)" .
This property represents a physical quantity of type "length" .
The minimum value for this property is "[0" .
The default value for this property is given by the conditional value expression "0" .
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 maxZ : "the truncation height (zero means no truncation)" .
This property represents a physical quantity of type "length" .
The minimum value for this property is "[0" .
The default value for this property is given by the conditional value expression "0" .
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 minRadius : "the radius of the central cavity" .
This property represents a physical quantity of type "length" .
The minimum value for this property is "[0" .
The default value for this property is given by the conditional value expression "0" .
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overrideprotectedvirtual |
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 \(R\). Substituting the exponential radial profile (without truncation) into this equation, we obtain
\[ {\cal{X}} = 1 - \left( 1+\frac{R}{h_R} \right) \exp \left( -\frac{R}{h_R} \right). \]
This equation can be solved by means of the Lambert function of order \(-1\), yielding
\[ R = h_R \left[ -1-W_{-1} \left( \frac{ {\cal{X}}-1}{\text{e}} \right) \right]. \]
The Lambert function \(W_{-1}(z)\) is implemented in the function SpecialFunctions::LambertW1. The truncation and the inner hole are taken into account by rejecting values larger than \(R_{\text{max}}\) or smaller than \(R_{\text{min}}\).
Implements SepAxGeometry.
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overrideprotectedvirtual |
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 exponential disk geometry, this integration is simple, and the inversion results in
\[ z = \begin{cases} \; h_z\,\ln(2{\cal{X}}) & \text{if $0<{\cal{X}}<\tfrac{1}{2}$,} \\ \;-h_z\,\ln[2(1-{\cal{X}})] & \text{if $\tfrac{1}{2}<{\cal{X}}<1$.} \end{cases} \]
The truncation is taken into account by rejecting values \(|z|\) larger than \(z_{\text{max}}\).
Implements SepAxGeometry.
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inline |
This function returns the value of the discoverable double property scaleHeight : "the scale height" .
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 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 verifies the validity of the parameters. The central density \(\rho_0\) is set by the normalization condition that the total mass equals one. One finds after some elementary calculus
\[ \frac{1}{\rho_0} = 4\pi\, h_R^2\, h_z \left( 1 - {\text{e}}^{-z_{\text{max}}/h_z} \right) \left[ \left( 1+\frac{R_{\text{min}}}{h_R} \right) {\text{e}}^{-R_{\text{min}}/h_R}- \left( 1+\frac{R_{\text{max}}}{h_R} \right) {\text{e}}^{-R_{\text{max}}/h_R} \right] . \]
In case there is no truncation in either radial or vertical directions and no inner hole, this reduces to
\[ \rho_0 = \frac{1}{ 4\pi\, h_R^2\, h_z }. \]
Reimplemented from SimulationItem.
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overrideprotectedvirtual |
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 exponential disc geometry we find
\[ \Sigma_R = \rho_0 h_R \left( {\text{e}}^{-R_{\text{min}}/h_R} - {\text{e}}^{-R_{\text{max}}/h_R} \right), \]
which reduces to \( \Sigma_R = \rho_0 h_R \) if there is no radial truncation and no inner hole.
Implements AxGeometry.
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overrideprotectedvirtual |
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 exponential disc geometry we find
\[ \Sigma_Z = 2\,\rho_0 h_Z \left( 1 - {\text{e}}^{-z_{\text{max}}/h_z} \right), \]
which reduces to \( \Sigma_Z = 2\,\rho_0 h_z \) if there is no vertical truncation. If there is an inner hole, obviously \(\Sigma_Z=0\).
Implements Geometry.