Thermodynamics of hyperon stars

Abstract

For a single-component perfect Fermi gas we used the numerical programme for the equation of state given by Bauer. For a star of hot non-degenerate neutron gas we calculated the deviations of the internal structure with regard to a totally degenerate neutron star. For a multi-component perfect gas with an exponential-type elementary particle spectrum we present the equation of state. The highest possible temperature is T0 = 2 x 101 2°K, where the total mass density diverges. For the central region of hyperon stars, in contrast to other authors, we can prove that the time component of the metric tensor has no singularity, and that the velocity of sound tends to zero (instead of rising above the velocity of light). INTRODUCTION We are studying the internal structure of hot neutron stars, which are in fact hyperon stars. Our main interest is directed towards the peculiar singularities in the centres of these stars. For this purpose we need an equation of state which can be used up to very high total energy densities (p>> 1014 g/cm3). The matter in such a state consists no longer of neutrons only, but also contains innumerable heavier particles and resonances. For in every elementary scattering process new particles can be produced if there is sufficient energy, and if the well-known conservation laws are not violated. Therefore detailed calculations of hot hyperon stars have to deal with the whole spectrum of elementary particles up to very high masses and their interactions. Hansen' has made a calculation, which is based on all particles with masses up to 1317 MeV (e, t, it, n, p, A, A, , ), taking into account the conservation laws of the number of baryons, of electronic leptons, muonic leptons and of the total charge. By using a variational approach he proves that, as higher densities are approached (p > 10175 g/cm3) the antiparticles as well as the leptons die out. Our aim was to continue Hansen's calculation up to even higher densities, which may occur in the central region of a heavy neutron star. We claim that it is not possible to restrict the calculations to a definite number of different elementary particles, but that the possible production of any particle of the whole particle spectrum has to be included. For example, free heavy resonances normally disintegrate quickly, yet this behaviour is no longer observed in a dense region, if the degenerate Fermi distribution of the resulting particle is already fully occupied. In the intermediate region the disintegration is greatly impeded, depending on the chemical potentials and temperature, T. 469