grmhd::AnalyticData::MagnetizedFmDisk Class Reference

Magnetized fluid disk orbiting a Kerr black hole. More...

#include <MagnetizedFmDisk.hpp>

Classes
struct	BFieldNormGridRes
	Grid resolution used in magnetic field normalization. More...
struct	InversePlasmaBeta
	The maximum-magnetic-pressure-to-maximum-fluid-pressure ratio. More...
struct	ThresholdDensity
	The rest mass density (in units of the maximum rest mass density in the disk) below which the matter in the disk is initially unmagetized. More...

Public Types
template<typename DataType >
using	tags = tmpl::push_back< typename gr::AnalyticSolution< 3 >::template tags< DataType >, hydro::Tags::RestMassDensity< DataType >, hydro::Tags::SpecificInternalEnergy< DataType >, hydro::Tags::Temperature< DataType >, hydro::Tags::Pressure< DataType >, hydro::Tags::SpatialVelocity< DataType, 3 >, hydro::Tags::MagneticField< DataType, 3 >, hydro::Tags::DivergenceCleaningField< DataType >, hydro::Tags::LorentzFactor< DataType >, hydro::Tags::SpecificEnthalpy< DataType > >
using	options = tmpl::push_back< FmDisk::options, ThresholdDensity, InversePlasmaBeta, BFieldNormGridRes >
using	equation_of_state_type = typename FmDisk::equation_of_state_type

Public Member Functions
	MagnetizedFmDisk (const MagnetizedFmDisk &)=default
MagnetizedFmDisk &	operator= (const MagnetizedFmDisk &)=default
	MagnetizedFmDisk (MagnetizedFmDisk &&)=default
MagnetizedFmDisk &	operator= (MagnetizedFmDisk &&)=default
	MagnetizedFmDisk (double bh_mass, double bh_dimless_spin, double inner_edge_radius, double max_pressure_radius, double polytropic_constant, double polytropic_exponent, double threshold_density, double inverse_plasma_beta, size_t normalization_grid_res=BFieldNormGridRes::suggested_value())
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
void	pup (PUP::er &) override
const equation_of_state_type &	equation_of_state () const
template<typename DataType , typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tags... >) const
	The variables in Cartesian Kerr-Schild coordinates at (x, t).
template<typename DataType , typename Tag >
tuples::TaggedTuple< Tag >	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tag >) const
	The variables in Cartesian Kerr-Schild coordinates at (x, t).
virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0

Static Public Attributes
static constexpr size_t	volume_dim = 3_st
static constexpr Options::String	help

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

Detailed Description

Magnetized fluid disk orbiting a Kerr black hole.

In the context of simulating accretion disks, this class implements a widely used (e.g. [73], [152], [190]) initial setup for the GRMHD variables, consisting of a Fishbone-Moncrief disk [64] (see also RelativisticEuler::Solutions::FishboneMoncriefDisk), threaded by a weak poloidal magnetic field. The magnetic field is constructed from an axially symmetric toroidal magnetic potential which, in Kerr ("spherical Kerr-Schild") coordinates, has the form

\begin{align*} A_\phi(r,\theta) \propto \text{max}(\rho(r,\theta) - \rho_\text{thresh}, 0), \end{align*}

where \(\rho_\text{thresh}\) is a user-specified threshold density that confines the magnetic flux to exist inside of the fluid disk only. A commonly used value for this parameter is \(\rho_\text{thresh} = 0.2\rho_\text{max}\), where \(\rho_\text{max}\) is the maximum value of the rest mass density in the disk. Using this potential, the Eulerian magnetic field takes the form

\begin{align*} B^r = \frac{F_{\theta\phi}}{\sqrt{\gamma}},\quad B^\theta = \frac{F_{\phi r}}{\sqrt{\gamma}},\quad B^\phi = 0, \end{align*}

where \(F_{ij} = \partial_i A_j - \partial_j A_i\) are the spatial components of the Faraday tensor, and \(\gamma\) is the determinant of the spatial metric. The magnetic field is then normalized so that the plasma- \(\beta\) parameter, \(\beta = 2p/b^2\), equals some value specified by the user. Here, \(p\) is the fluid pressure, and

\begin{align*} b^2 = b^\mu b_\mu = \frac{B_iB^i}{W^2} + (B^iv_i)^2 \end{align*}

is the norm of the magnetic field in the fluid frame, with \(v_i\) being the spatial velocity, and \(W\) the Lorentz factor.

Note

When using Kerr-Schild coordinates, the horizon that is at constant \(r\) is not spherical, but instead spheroidal. This could make application of boundary condition and computing various fluxes across the horizon more complicated than they need to be. Thus, similar to RelativisticEuler::Solutions::FishboneMoncriefDisk we use Spherical Kerr-Schild coordinates, see gr::Solutions::SphericalKerrSchild, in which constant \(r\) is spherical. Because we compute variables in Kerr-Schild coordinates, there is a necessary extra step of transforming them back to Spherical Kerr-Schild coordinates.

Warning

Spherical Kerr-Schild coordinates and "spherical Kerr-Schild" coordinates are not same.

Member Function Documentation

get_clone()

auto grmhd::AnalyticData::MagnetizedFmDisk::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::MagnetizedFmDisk::help

staticconstexpr

Initial value:

= {
      "Magnetized Fishbone-Moncrief disk."}

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

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