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A polytrope with index n = 3 is a good model for the cores of white dwarfs of higher masses, according to the equation of state of relativistic degenerate matter. [7] A polytrope with index n = 3 is usually also used to model main-sequence stars like the Sun, at least in the radiation zone, corresponding to the Eddington standard model of ...
where is a dimensionless radius and is related to the density, and thus the pressure, by = for central density .The index is the polytropic index that appears in the polytropic equation of state, = + where and are the pressure and density, respectively, and is a constant of proportionality.
Some specific values of n correspond to particular cases: = for an isobaric process, = + for an isochoric process. In addition, when the ideal gas law applies: = for an isothermal process,
This yields a polytrope of index 3, which has a total mass, M limit, depending only on K 2. [9] For a fully relativistic treatment, the equation of state used interpolates between the equations P = K 1 ρ 5/3 for small ρ and P = K 2 ρ 4/3 for large ρ. When this is done, the model radius still decreases with mass, but becomes zero at M limit.
A similar situation occurs for accurate calculations of the pressure equation of state. Finally, the nuclear energy generation rate is computed from nuclear physics experiments, using reaction networks to compute reaction rates for each individual reaction step and equilibrium abundances for each isotope in the gas. [6] [8]
A polygon is a 2-dimensional polytope. Polygons can be characterised according to various criteria. Some examples are: open (excluding its boundary), bounding circuit only (ignoring its interior), closed (including both its boundary and its interior), and self-intersecting with varying densities of different regions.
However, this equation of state continues to be widely used in models of solid explosives. Of more elaborate equations of state, the most used in earth physics is the Birch–Murnaghan equation of state. In shock physics of metals and alloys, another widely used equation of state is the Mie–Gruneisen equation of state.
In metric theories of gravitation, particularly general relativity, a static spherically symmetric perfect fluid solution (a term which is often abbreviated as ssspf) is a spacetime equipped with suitable tensor fields which models a static round ball of a fluid with isotropic pressure.