2.4 Numerical Schemes2 The Equilibrium Structure of 2.2 Geometry of Space-Time

2.3 Equations of State

The simplest equation of state one can use to model relativistic stars is the relativistic polytropic EOS [5]



where tex2html_wrap_inline2001 is the rest mass density, K is a constant, and tex2html_wrap_inline2005 is the polytropic exponent. Instead of tex2html_wrap_inline2005, one often uses the polytropic index N, defined through


For this equation of state, the quantity tex2html_wrap_inline2011 has units of length. In gravitational units (c = G =1), one can thus use tex2html_wrap_inline2015 as a fundamental length scale to define dimensionless quantities. Equilibrium models are then characterized by the polytropic index N and their properties can be scaled to different values, using an appropriate value for K . For N <1.0 (N >1.0), one obtains stiff (soft) models, while for N =0.5 - 1.0, one obtains models with bulk properties that are comparable to those of observed neutron stars.

Note that for the above polytropic EOS, the polytropic index tex2html_wrap_inline2005 coincides with the adiabatic index of a relativistic isentropic fluid


This is not the case for the polytropic equation of state, tex2html_wrap_inline2029, that has been used by other authors, which satisfies (12Popup Equation) only in the Newtonian limit.

The true equation of state that describes the interior of compact stars is largely unknown. This results from the inability to verify experimentally the different theories that describe the strong interactions between baryons and the many-body theories of dense matter at densities larger than about twice the nuclear density (i.e. at densities larger than about tex2html_wrap_inline2031).

To date, many different realistic EOSs have been proposed which produce neutron stars that satisfy the currently available observational constraints (Currently, the two main constraints are that the EOS must admit nonrotating neutron stars with gravitational mass of at least tex2html_wrap_inline2033 and allow rotational periods at least as small as 1.56 ms, see [6Jump To The Next Citation Point In The Article, 7Jump To The Next Citation Point In The Article].). The proposed EOSs are qualitatively and quantitatively very different from each other. Some are based on relativistic many-body theories, while others use nonrelativistic theories with baryon-baryon interaction potentials. A classic collection of early proposed EOSs was compiled by Arnett and Bowers [8Jump To The Next Citation Point In The Article], while recent EOSs are described in Salgado et al. [9Jump To The Next Citation Point In The Article].

High density equations of state with pion condensation have been proposed by Migdal [10] and Sawyer and Scalapino [11]. The possibility of Kaon condensation is discussed by Brown and Bethe [12Jump To The Next Citation Point In The Article] and questioned by Pandharipande et al. [13]. Many authors have examined the possibility of stars composed of strange quark matter, and a recent review can be found in [14].

The realistic EOSs are supplied in the form of an energy density vs. pressure table, and intermediate values are interpolated. This results in some loss of accuracy because the usual interpolation methods do not preserve thermodynamical consistency. Recently however, Swesty [15] devised a cubic Hermite interpolation scheme that does preserve thermodynamical consistency; the scheme has been shown to indeed produce higher accuracy neutron star models in Nozawa et al. [16Jump To The Next Citation Point In The Article].

2.4 Numerical Schemes2 The Equilibrium Structure of 2.2 Geometry of Space-Time

image Rotating Stars in Relativity
Nikolaos Stergioulas
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to livrev@aei-potsdam.mpg.de