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 = EquationsOfState::EquationOfState< true, 1 >

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
virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0

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