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 = implementation defined
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

$$\begin{array}{rl}|B_{\mathrm{C}\mathrm{G}\mathrm{S}}|& =\sqrt{4\pi b^2}\left(\frac{c^2}{G{M}_{\odot }}\right)\left(\frac{c}{\sqrt{4\pi {ϵ}_{0}G}}\right)\\ & =\sqrt{b^2}\times 8.352\times {10}^{19}\mathrm{G}.\end{array}$$

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

• ${\rho }_c(0)=1.28\times {10}^{-3}$
• $K=100$
• $\mathrm{\Gamma }=2$
• Domain $[-20,20{]}^3$
• Units $M=M_{\odot }$
• A target final time 20ms means $20\times {10}^{-3}/(5\times {10}^{-6})=4000M$
• The mass of the star is $1.4M_{\odot }$

Parameters for desired magnetic field strength:

• For $n_s=0$ and $p_{\mathrm{c}\mathrm{u}\mathrm{t}}=0.04p_{max}$ setting $A_b=6\times {10}^{-5}$ yields a maximum mganetic field strength of $1.002\times {10}^{16}G$.
• For $n_s=1$ and $p_{\mathrm{c}\mathrm{u}\mathrm{t}}=0.04p_{max}$ setting $A_b=0.4$ yields a maximum mganetic field strength of $1.05\times {10}^{16}G$.
• For $n_s=2$ and $p_{\mathrm{c}\mathrm{u}\mathrm{t}}=0.04p_{max}$ setting $A_b=2500$ yields a maximum mganetic field strength of $1.03\times {10}^{16}G$.
• For $n_s=3$ and $p_{\mathrm{c}\mathrm{u}\mathrm{t}}=0.04p_{max}$ setting $A_b=1.65\times {10}^7$ yields a maximum mganetic field strength of $1.07\times {10}^{16}G$.

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.

---

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

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