A static spherically symmetric star in Newtonian gravity. More...

#include <LaneEmdenStar.hpp>

Classes
struct	CentralMassDensity
	The central mass density of the star. More...

struct	PolytropicConstant
	The polytropic constant of the polytropic fluid. More...

Public Types
using	equation_of_state_type = EquationsOfState::PolytropicFluid< false >

using	options = tmpl::list< CentralMassDensity, PolytropicConstant >

Public Member Functions
	LaneEmdenStar (const LaneEmdenStar &)=default

LaneEmdenStar &	operator= (const LaneEmdenStar &)=default

	LaneEmdenStar (LaneEmdenStar &&)=default

LaneEmdenStar &	operator= (LaneEmdenStar &&)=default

auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override

	LaneEmdenStar (double central_mass_density, double polytropic_constant)

template<typename DataType , typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const tnsr::I< DataType, 3 > &x, const double, tmpl::list< Tags... >) const
	Retrieve a collection of variables at `(x, t)`

template<typename DataType >
tnsr::I< DataType, 3 >	gravitational_field (const tnsr::I< DataType, 3 > &x) const
	Compute the gravitational field for the corresponding source term, LaneEmdenGravitationalField. More...

const EquationsOfState::PolytropicFluid< false > &	equation_of_state () const

void	pup (PUP::er &) override

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

Static Public Attributes
static constexpr Options::String	help

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

Detailed Description

A static spherically symmetric star in Newtonian gravity.

The solution for a static, spherically-symmetric star in 3 dimensions, found by solving the Lane-Emden equation [36] [163] . The Lane-Emden equation has closed-form solutions for certain equations of state; this class implements the solution for a polytropic fluid with polytropic exponent \(\Gamma=2\) (i.e., with polytropic index \(n=1\)). The solution is returned in units where \(G=1\), with \(G\) the gravitational constant.

The radius and mass of the star are determined by the polytropic constant \(\kappa\) and central density \(\rho_c\). The radius is \(R = \pi \alpha\), and the mass is \(M = 4 \pi^2 \alpha^3 \rho_c\), where \(\alpha = \sqrt{\kappa / (2 \pi)}\) and \(G=1\).

Member Function Documentation

◆ get_clone()

auto NewtonianEuler::Solutions::LaneEmdenStar::get_clone ( ) const -> std::unique_ptr< evolution::initial_data::InitialData >

overridevirtual

Implements evolution::initial_data::InitialData.

◆ gravitational_field()

template<typename DataType >

tnsr::I< DataType, 3 > NewtonianEuler::Solutions::LaneEmdenStar::gravitational_field ( const tnsr::I< DataType, 3 > & x ) const

Compute the gravitational field for the corresponding source term, LaneEmdenGravitationalField.

The result is the vector-field giving the acceleration due to gravity that is felt by a test particle.

Member Data Documentation

◆ help

constexpr Options::String NewtonianEuler::Solutions::LaneEmdenStar::help

staticconstexpr

Initial value:

= {
      "A static, spherically-symmetric star in Newtonian gravity, found by\n"
      "solving the Lane-Emden equations, with a given central density and\n"
      "polytropic fluid. The fluid has polytropic index 1, but the polytropic\n"
      "constant is specifiable"}

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

src/PointwiseFunctions/AnalyticSolutions/NewtonianEuler/LaneEmdenStar.hpp

Classes

Public Types

Public Member Functions

Static Public Attributes