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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 \(G=1\).

Member Function Documentation

◆ 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.

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 files: