grmhd::AnalyticData::MagnetizedTovStar Class Reference

Magnetized TOV star initial data, where metric terms only account for the hydrodynamics not the magnetic fields. More...

#include <MagnetizedTovStar.hpp>

Classes
struct	MagneticFields

Public Types
using	options = tmpl::push_back<tov_star::options, MagneticFields>
template<typename DataType>
using	tags = typename tov_star::template tags<DataType>
using	equation_of_state_type

Public Member Functions
	MagnetizedTovStar (const MagnetizedTovStar &rhs)
MagnetizedTovStar &	operator= (const MagnetizedTovStar &rhs)
	MagnetizedTovStar (MagnetizedTovStar &&)
MagnetizedTovStar &	operator= (MagnetizedTovStar &&)
	MagnetizedTovStar (double central_rest_mass_density, std::unique_ptr< EquationsOfState::EquationOfState< true, 1 > > equation_of_state, RelativisticEuler::Solutions::TovCoordinates coordinate_system, std::vector< std::unique_ptr< grmhd::AnalyticData::InitialMagneticFields::InitialMagneticField > > magnetic_fields)
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 variables at (x)
void	pup (PUP::er &p) override
const EquationsOfState::EquationOfState< true, 1 > &	equation_of_state () const
Public Member Functions inherited from evolution::initial_data::InitialData
virtual const InitialData &	unwrap () const
	Unwrap wrapper types (e.g. WithNoise, which wraps analytic initial data and adds random noise) to reach the underlying analytic solution or data.

Static Public Attributes
static constexpr Options::String	help = {"Magnetized TOV star."}
static constexpr size_t	volume_dim = 3_st

Protected Attributes
std::vector< std::unique_ptr< grmhd::AnalyticData::InitialMagneticFields::InitialMagneticField > >	magnetic_fields_ {}

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

Detailed Description

Magnetized TOV star initial data, where metric terms only account for the hydrodynamics not the magnetic fields.

Superposes magnetic fields on top of a TOV solution. These can be any of the classes derived from grmhd::AnalyticData::InitialMagneticFields::InitialMagneticField

Conversion to CGS units and values for poloidal magnetic field

While the amplitude \(A_b\) is specified in the code, it is more natural to work with the magnetic field strength, which is given by \(\sqrt{b^2}\) (where \(b^a\) is the comoving magnetic field), and in CGS units is

\begin{align*} |B_{\mathrm{CGS}}|&= \sqrt{4 \pi b^2} \left(\frac{c^2}{G M_\odot}\right) \left(\frac{c}{\sqrt{4 \pi \epsilon_0 G}}\right) \\ &= \sqrt{b^2} \times 8.352\times10^{19}\mathrm{G} \,. \end{align*}

We now give values used for standard tests of magnetized stars with a poloidal magnetic field.

• \(\rho_c(0)=1.28\times10^{-3}\)
• \(K=100\)
• \(\Gamma=2\)
• Domain \([-20,20]^3\)
• Units \(M=M_\odot\)
• A target final time 20ms means \(20\times10^{-3}/(5\times10^{-6})=4000M\)
• The mass of the star is \(1.4M_{\odot}\)

Parameters for desired magnetic field strength:

• For \(n_s=0\) and \(p_{\mathrm{cut}}=0.04p_{\max}\) setting \(A_b=6\times10^{-5}\) yields a maximum mganetic field strength of \(1.002\times10^{16}G\).
• For \(n_s=1\) and \(p_{\mathrm{cut}}=0.04p_{\max}\) setting \(A_b=0.4\) yields a maximum mganetic field strength of \(1.05\times10^{16}G\).
• For \(n_s=2\) and \(p_{\mathrm{cut}}=0.04p_{\max}\) setting \(A_b=2500\) yields a maximum mganetic field strength of \(1.03\times10^{16}G\).
• For \(n_s=3\) and \(p_{\mathrm{cut}}=0.04p_{\max}\) setting \(A_b=1.65\times10^{7}\) yields a maximum mganetic field strength of \(1.07\times10^{16}G\).

Note that the magnetic field strength goes as \(A_b\) so any desired value can be achieved by a linear scaling.

Member Function Documentation

get_clone()

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

overridevirtual

Implements evolution::initial_data::InitialData.

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

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