| The central density of neutron stars formed in supernova is on the order of 1015g/(cm)3, which is a density higher than the nuclear density ρnua≈2.8 ×1014g/(cm)3. The structure of neutron stars, and the relation between their masses and radii, are determined by the equation of state (EOS) of the matter. However, the EOS of matter beyond the nuclear density is not well understood at the moment. Many different treatments (e.g., the mean field theory, liquid drop treatment etc.) have been proposed for the construction of the EOS of neutron stars and proto-neutron stars, leading to many different so-called "realistic EOS tables". In this thesis, we use 4 different such EOS tables (the Lattimer-Swesty EOS, the H. Shen EOS, the M. Hempel EOS and the G. Shen EOS) to construct equilibrium configurations of neutron stars and study the effects of temperature on the structure and the stability, based on the Tolman-Oppenheimer-Volkoff equations.EOS in table form is inconvenient for the study of their properties. Read J.S. et. al. proposed a treatment expressing EOS tables of zero temperature in piecewise polytropic forms, P=Kpγ, where P is the pressure, p is rest mass density and K and γ take different values at different ranges of p. They demonstrated that the piecewise polytropic treament is capable of expressing many different EOS tables of zero temperature. In this thesis, we extended the piecewise polytropic treament to non-zero temperature. We showed that finite temperature EOS tables can be expressed as two sets of piecewise polytropes, one for P and one for the internal energy u, in terms of the p and the T (the temperature). We showed that the 4 finite temperature EOS’s studied (Lattimer-Swesty EOS, the H. Shen EOS, the M. Hempel EOS and the G. Shen EOS) can all be accurately expressed in piecewise polytropic forms. In particular, we compared the equilibrium configurations of neutron star and proto-neutron star constructed using the EOS tables and the piecewise polytropic forms. |
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