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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 <BrokenExpDiskGeometry.hpp>
Public Member Functions | |
| double | breakRadius () const |
| double | scaleHeight () const |
| double | scaleLengthInner () const |
| double | scaleLengthOuter () const |
| double | sharpness () 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 | |
| BrokenExpDiskGeometry () | |
| 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 = BrokenExpDiskGeometry |
Private Member Functions | |
| double | radialDensity (double R) const |
Private Attributes | |
| double | _beta |
| double | _breakRadius |
| const double & | _hinn |
| const double & | _hout |
| const double & | _hz |
| const double & | _Rb |
| double | _rho0 |
| Array | _Rv |
| const double & | _s |
| double | _scaleHeight |
| double | _scaleLengthInner |
| double | _scaleLengthOuter |
| double | _sharpness |
| double | _SigmaR |
| Array | _Xv |
Friends | |
| class | ItemRegistry |
The BrokenExpDiskGeometry class is a subclass of the SepAxGeometry class. It describes a particular class of models for discs with a so-called break in the radial profile. More specifically, the radial density profile is a broken exponential profile: an inner exponential profile with scale length \(h_{R,{\text{inn}}}\) and an outer exponential profile with scale length \(h_{R,{\text{out}}}\). There is no limitation in the nature of the break: the inner profile can be shallower than the outer one ( \(h_{R,{\text{out}}} < h_{R,{\text{inn}}}\)) or steeper ( \(h_{R,{\text{out}}} > h_{R,{\text{inn}}}\)). These two asymptotic profiles are joined smoothly at a break radius \(R_{\text{b}}\), with a dimensionless parameter \(s\) that sets the smoothness of the transition between these two regimes. For large values of the smoothness parameter, \(s\gg1\), the transition is sharp, whereas for small values, \(s\sim1\), the transition is very gradual. In the vertical direction, the density decreases exponentially. No truncation is applied. In formula form,
\[ \rho(R,z) = \rho_0 {\text{e}}^{-\frac{R}{h_{\text{inn}}}-\frac{|z|}{h_z}} \left( 1 + {\text{e}}^{\frac{s\,(R-R_{\text{b}})}{h_{\text{out}}}} \right)^{\frac{1}{s} \left(\frac{h_{\text{out}}}{h_{\text{inn}}} - 1\right)}. \]
This geometry is strongly inspired by Erwin et al. (2008, AJ, 135, 20) and Erwin (2015, ApJ, 799, 226), but has one significant difference: in our formulation, the sharpness \(s\) is a dimensionless number, whereas in Erwin et al. (2008) the sharpness parameter \(\alpha\) is a quantity with dimension length \(^{-1}\). More specifically,
\[ \alpha = \frac{s}{h_{\text{out}}} \]
The model contains five free parameters: the scale length of inner disc \(h_{\text{inn}}\), the scale length of outer disc \(h_{\text{out}}\), the scale height \(h_z\), the break radius \(R_{\text{b}}\), and the sharpness of the break \(s\). The final parameter that appears in the formula above is the central density \(\rho_0\); it is not a free parameter, but such that the total mass of the geometry is normalized to one.
This item type 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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inlineprotected |
Default constructor for concrete Item subclass BrokenExpDiskGeometry : "a broken exponential disk geometry" .
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inline |
This function returns the value of the discoverable double property breakRadius : "the break radius" .
This property represents a physical quantity of type "length" .
The minimum value for this property is "]0" .
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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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private |
This private member function returns the radial part of the density distribution, i.e.
\[ \rho_R(R) = {\text{e}}^{-\frac{R}{h_{\text{inn}}}} \left( 1 + {\text{e}}^{\frac{s\,(R-R_{\text{b}})}{h_{\text{out}}}} \right)^{\frac{1}{s} \left(\frac{h_{\text{out}}}{h_{\text{inn}}} - 1\right)} \]
It is just an auxiliary function.
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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 \({\cal{X}}\). We just use the vector of cumulative masses stored internally.
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
\[ z = \begin{cases} \; h_z\,\ln(2{\cal{X}}) & \text{if $0<{\cal{X}}<\tfrac{1}{2}$,} \\ \;-h_z\,\ln[2(1-{\cal{X}})] & \text{if $\tfrac{1}{2}<{\cal{X}}<1$.} \end{cases} \]
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 scaleLengthInner : "the scale length of the inner disk" .
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 scaleLengthOuter : "the scale length of the outer disk" .
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 equals one. One finds after some elementary calculus
\[ \rho_0 = \frac{1}{4\pi\,h_z\, I_R} \]
where \( I_R\) is the integral
\[ I_R = \int_0^\infty \rho_R(R)\,R\, {\text{d}}R \]
with \(\rho_R(R)\) the radial part of the density distribution. This integral is calculated using a simple trapezoidal integration. This routine immediately also stores the cumulative radial distribution
\[ X(R) = \frac{1}{I_R} \int_0^R \rho_R(R')\, R'\, {\text{d}}R' \]
in an internal array, so that this can be used later on to generate random positions extracted from this geometry. Finally, also the radial surface density is calculated using a similar numerical integration.
Reimplemented from SimulationItem.
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inline |
This function returns the value of the discoverable double property sharpness : "the sharpness of the break" .
The minimum value for this property is "]0" .
The default value for this property is given by the conditional value expression "3" .
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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.
\[ \Sigma_R = \int_0^\infty \rho(R,z)\, {\text{d}}R. \]
This value is calculated numerically during setup and stored as a data member.
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,
\[ \Sigma_Z = \int_{-\infty}^\infty \rho(0,z)\, {\text{d}} z \]
For the BrokenExpDiskGeometry model, one obtains
\[ \Sigma_Z = 2\, \rho_0\, z_0 \left(1+{\text{e}}^{-s\,R_{break}}\right)^{\frac{1}{s} \left(\frac{h_{\text{out}}}{h_{\text{inn}}} - 1\right)}\]
Implements Geometry.