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SpECTRE
v2026.04.01
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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. | |
| const EquationsOfState::PolytropicFluid< false > & | equation_of_state () const |
| void | pup (PUP::er &) override |
Static Public Attributes | |
| static constexpr Options::String | help |
Friends | |
| bool | operator== (const LaneEmdenStar &lhs, const LaneEmdenStar &rhs) |
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 [40] [185] . 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 \(G=1\).
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overridevirtual |
Implements evolution::initial_data::InitialData.
| 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.
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staticconstexpr |