Abstract.The structure of neutron stars is determined by the equation of state of dense matter in their interiors. Brief review of the equation of state from neutron star surface to its center is presented. Recent discovery of two two-solar-mass pulsars puts interesting constraints on the poorly known equation of state of neutron-star cores for densities greater than normal nuclear matter density. Namely, this equation of state has to be stiff enough to yield maximum allowable mass of neutron stars greater than two solar masses. There are many models of neutron stars cores involving exclusively nucleons that satisfy this constraint. However, for neutron-star models based on recent realistic baryon interaction, and allowing for the presence of hyperons, the hyperon softening of the equation of state yields maximum masses significantly lower than two solar masses. Proposed ways out from this "hyperon puzzle" are presented. They require a very fine tuning of parameters of dense hadronic matter and quark matter models. Consequences for the mass-radius relation for neutron stars are illustrated. A summary of the present situation and possible perspectives/challenges, as well as possible observational tests, are given.
IntroductionThe equation of state (EOS) of neutron stars (NS) is one of their mysteries. For astrophysically interesting masses, M > M ⊙ , and for NS which are older than a year, the effects of temperature, magnetic field, and of rotation, on the NS structure are small [1], and will be neglected here. Then, the structure of NS, and in particular their maximum allowable mass, M max , is determined by the EOS [1].To construct models of NS, from the surface (or rather from an atmosphere, which is however typically only a few cm thick) to the star's center, we need the EOS for density from a fraction of g cm −3 up to some 5 × 10 15 g cm −3 . A general overview of theoretical EOSs for NS, from the surface to the center, is given in Sect. 2.As we stress in Sect. 2, at density larger than 10 6 g cm −3 , matter in NS is strongly degenerate, and therefore pressure becomes a function of the density only, P = P (ρ). Up to the normal nuclear density ρ 0 = 2.7 × 10 14 g cm −3 , corresponding to the baryon (number) density n 0 = 0.16 fm −3 , the EOS is rather well established [2]. However, for ρ > ρ 0 the uncertainty in the EOS increases rapidly with increasing ρ. This uncertainty is reflected in the uncertainty in the theoretical prediction for M max , which is the functional of P (ρ):