NewtonianEuler::Solutions::LaneEmdenStar Class Reference

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 source_term_type = Sources::LaneEmdenGravitationalField

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

## Public Member Functions

LaneEmdenStar (const LaneEmdenStar &)=delete

LaneEmdenStaroperator= (const LaneEmdenStar &)=delete

LaneEmdenStar (LaneEmdenStar &&) noexcept=default

LaneEmdenStaroperator= (LaneEmdenStar &&) noexcept=default

LaneEmdenStar (double central_mass_density, double polytropic_constant) noexcept

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

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

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

const Sources::LaneEmdenGravitationalFieldsource_term () const noexcept

void pup (PUP::er &) noexcept

## Static Public Attributes

static constexpr Options::String help

## Friends

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

## 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 [13] [59] . 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 $$G=1$$.

## ◆ gravitational_field()

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

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.

## ◆ 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 files:
• src/PointwiseFunctions/AnalyticSolutions/NewtonianEuler/LaneEmdenStar.hpp
• src/PointwiseFunctions/AnalyticSolutions/NewtonianEuler/LaneEmdenStar.cpp