grmhd::AnalyticData::BondiHoyleAccretion Class Reference

Analytic initial data for axially symmetric Bondi-Hoyle accretion. More...

#include <BondiHoyleAccretion.hpp>

Classes
struct	BhDimlessSpin
	The dimensionless black hole spin, $a_{\ast }=a/M$. More...
struct	BhMass
	The mass of the black hole, $M$. More...
struct	FlowSpeed
	The magnitude of the spatial velocity far from the black hole. More...
struct	MagFieldStrength
	The strength of the magnetic field. More...
struct	PolytropicConstant
	The polytropic constant of the fluid. More...
struct	PolytropicExponent
	The polytropic exponent of the fluid. More...
struct	RestMassDensity
	The rest mass density of the fluid far from the black hole. More...

Public Types
using	equation_of_state_type = EquationsOfState::PolytropicFluid< true >
using	options = implementation defined
Public Types inherited from grmhd::AnalyticDataBase
template<typename DataType >
using	tags = implementation defined

Public Member Functions
	BondiHoyleAccretion (const BondiHoyleAccretion &)=default
BondiHoyleAccretion &	operator= (const BondiHoyleAccretion &)=default
	BondiHoyleAccretion (BondiHoyleAccretion &&)=default
BondiHoyleAccretion &	operator= (BondiHoyleAccretion &&)=default
	BondiHoyleAccretion (double bh_mass, double bh_dimless_spin, double rest_mass_density, double flow_speed, double magnetic_field_strength, double polytropic_constant, double polytropic_exponent)
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
template<typename DataType , typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tags... >) const
	Retrieve a collection of hydro variables at x
template<typename DataType , typename Tag , Requires< not tmpl::list_contains_v< tmpl::push_back< hydro::grmhd_tags< DataType >, hydro::Tags::SpecificEnthalpy< DataType > >, Tag > > = nullptr>
tuples::TaggedTuple< Tag >	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tag >) const
	Retrieve the metric variables at x
void	pup (PUP::er &) override
const EquationsOfState::PolytropicFluid< true > &	equation_of_state () const
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::RestMassDensity< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::RestMassDensity< DataType > >
	Retrieve hydro variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::ElectronFraction< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::ElectronFraction< DataType > >
	Retrieve hydro variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::SpecificInternalEnergy< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::SpecificInternalEnergy< DataType > >
	Retrieve hydro variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::Temperature< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::Temperature< DataType > >
	Retrieve hydro variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::Pressure< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::Pressure< DataType > >
	Retrieve hydro variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::SpatialVelocity< DataType, 3 > >) const -> tuples::TaggedTuple< hydro::Tags::SpatialVelocity< DataType, 3 > >
	Retrieve hydro variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::MagneticField< DataType, 3 > >) const -> tuples::TaggedTuple< hydro::Tags::MagneticField< DataType, 3 > >
	Retrieve hydro variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::DivergenceCleaningField< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::DivergenceCleaningField< DataType > >
	Retrieve hydro variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::LorentzFactor< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::LorentzFactor< DataType > >
	Retrieve hydro variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::SpecificEnthalpy< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::SpecificEnthalpy< DataType > >
	Retrieve hydro variable at x
virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0

Static Public Attributes
static constexpr Options::String	help
Static Public Attributes inherited from grmhd::AnalyticDataBase
static constexpr size_t	volume_dim = 3_st

Friends
bool	operator== (const BondiHoyleAccretion &lhs, const BondiHoyleAccretion &rhs)

Detailed Description

Analytic initial data for axially symmetric Bondi-Hoyle accretion.

In the context of studying Bondi-Hoyle accretion, i.e. non-spherical accretion on to a Kerr black hole moving relative to a gas cloud, this class implements the method proposed by [71] to initialize the GRMHD variables. The fluid quantities are initialized with their (constant) values far from the black hole, e.g. $\rho ={\rho }_{\mathrm{\infty }}$. Here we assume a polytropic equation of state, so only the rest mass density, as well as the polytropic constant and the polytropic exponent, are provided as inputs. The spatial velocity is initialized using a field that ensures that the injected gas reproduces a continuous parallel wind at large distances. The direction of this flow is chosen to be along the black hole spin. In Kerr (or "spherical Kerr-Schild", see gr::KerrSchildCoords) coordinates,

$$\begin{array}{rl}{v}^r& =\frac{1}{\sqrt{{\gamma }_{rr}}}{v}_{\mathrm{\infty }}\cos \theta \\ v^{\theta }& =-\frac{1}{\sqrt{{\gamma }_{\theta \theta }}}{v}_{\mathrm{\infty }}\sin \theta \\ v^{\varphi }& =0.\end{array}$$

where ${\gamma }_{ij}=g_{ij}$ is the spatial metric, and $v_{\mathrm{\infty }}$ is the flow speed far from the black hole. Note that $v_{\mathrm{\infty }}^2=v_i{v}^i$. Finally, following the work by [162], the magnetic field is initialized using Wald's solution to Maxwell's equations in Kerr black hole spacetime. In Kerr ("spherical Kerr-Schild") coordinates, the spatial components of the Faraday tensor read

$$\begin{array}{rl}{F}_{r\theta }& =a{B}_0[1+\frac{2Mr}{{\mathrm{\Sigma }}^2}(r^2-a^2)]\sin \theta \cos \theta \\ F_{\theta \varphi }& =B_0[\mathrm{\Delta }+\frac{2Mr}{{\mathrm{\Sigma }}^2}(r^4-a^4)]\sin \theta \cos \theta \\ F_{\varphi r}& =-B_0[r+\frac{M{a}^2}{{\mathrm{\Sigma }}^2}(r^2-a^2{\cos }^2\theta )(1+{\cos }^2\theta )]{\sin }^2\theta .\end{array}$$

where $\mathrm{\Sigma }=r^2+a^2{\cos }^2\theta$ and $\mathrm{\Delta }=r^2-2Mr+a^2$. The associated Eulerian magnetic field is

$$\begin{array}{r}{B}^r=\frac{F_{\theta \varphi }}{\sqrt{\gamma }},B^{\theta }=\frac{F_{\varphi r}}{\sqrt{\gamma }},B^{\varphi }=\frac{F_{r\theta }}{\sqrt{\gamma }}.\end{array}$$

where $\gamma =\text{det}({\gamma }_{ij})$. Wald's solution reproduces a uniform magnetic field far from the black hole.

Member Function Documentation

get_clone()

auto grmhd::AnalyticData::BondiHoyleAccretion::get_clone ( ) const -> std::unique_ptr< evolution::initial_data::InitialData >

overridevirtual

Implements evolution::initial_data::InitialData.

Member Data Documentation

help

constexpr Options::String grmhd::AnalyticData::BondiHoyleAccretion::help

staticconstexpr

Initial value:

= {
      "Axially symmetric accretion on to a Kerr black hole."}

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The documentation for this class was generated from the following file:

• src/PointwiseFunctions/AnalyticData/GrMhd/BondiHoyleAccretion.hpp