Neutron Star Matter At Finite Temperature

This article studies neutron star matter at finite temperature in the framework of the relativistic mean field theory.Firstly, we investigate the influence of the temperature on the stability of protoneutron stars. After the supernova, if the temperature is higher, a stable protoneutron is more difficult to be formed. A protoneutron star with too large mass (or total baryon number) will subside into a low mass black hole after the deleptonization. With the increase of the temperature, the subsidence from a protoneutron star into a black hole is more likely to happen. However, there exists a critical temperature value. If the temperature is higher than this critical value, the protoneutron star can not be formed and the subsidence from a protoneutron star into a black hole can not happen. The SN1987A is a potential evidence to prove that a more massive protoneutron star could subside into a black hole. If a protoneutron star does be born in the SN1987A, with the increase of the temperature, the subsidence into a black hole becomes more likely to take place. However, if the temperature is too high, the subsidence into a black hole can not happen. So, the information about the temperature from the observations is helpful for us to know the mechanics of some phenomenons such as SN1987A.Secondly, we study thermal protoneutron star matter with theδmeson by two steps. At the first step, we include hyperons in protoneutron star matter. Resutls show that after including theδmeson, (1) the effective masses of baryons with the same speice but different isospin states becomes splitted, (2) the critical densities for hyperons becomes lower and the amount of hyperons increases, (3) the neutrino aubundance decreases. The mainδmeson effects depend on the density and temperature. With the increase of the density, the mainδmeson effects increases first then decreases. The density range where theδmeson has obvious effects is just the core range of protoneutron stars. With the increase of the temperature, the mainδmeson effects are highly suppressed and the density range where theδmeson effects are obvious is narrowed. At the second step, we take account into the quark phase. The MIT bag model is used to describe the quark phase. With the increase of the temperature, the threshold densities for the hadron-quark phase transition become lower. If the bag constant is larger, the threshold density for the phase transition is less sensitive to the temperature. With the inclusion of theδmeson, the threshold densities for the phase transition become lower. Meanwhile, the influences of theδmeson on the phase transition are suppressed by the rise of the temperature. If the bag constant is larger, theδmeson effect is more obvious. Whether a protoneutron star can contain the quark content depends on the chosen of the bag constant.Thirdly, we study the direct Urca processes in neutron stars with hyperons. We not only calculate the direct Urca processes from nucleons but also calculate the processes from hyperons. Moreover, we take account into the contribution of theδmeson. With the increase of the density, the total energy loss does not change monotonously. At some densities, the total energy loss increases discontinuously. This indicates that in some positions in the neutron star, the heat may accumulate during the cooling process, which may lead to the instability. Compared with the condition that only nucleons are included, the inclusion of the hyperons make the total energy loss increase and the number of positions where the total energy loss increases discontinuously become more. It means the contribution of hyperons make neutron star cool faster and be more likely to become unstable.The neutrino luminosity increases with the star mass first then decreases. In the critical mass range, the same neutrino luminosity corresponds to two different masses. After including theδmeson, the threshold densities for the direct Urca processes will become lower, and enery loss caused by the drect Urca processes will increase. With the inclusion of theδmeson, at relative low densities, the total energy loss becomes much larger, namely, changes by 150%. As the density increases, the total energy loss with theδmeson is closer and closer to that without theδmeson. Moreover, with the inclusion of theδmeson, the neutrino luminosity increases. For M=1.4 M sun, it changes by 75% and will change more if the mass is larger.Finally, we study compact matter with a weak YY interaction at finite temperature. Results show that with the increase of the temperature, (1) the energy per baryon in strange hadronic matter increases, (2) the saturated density of strange hadronic matter increases, (3)the neutron star maximum mass increases and the stable mass range is narrowed,(4)the hyperon abundance in the star with the maximum mass increases first then decreases and more species of hyperons can appear in it. When the temperature is higher than 21MeV, with the weak YY interaction or with no (σ*,φ) mesons included, strange hadronic matter can not have a bound state. When the temperature is higher than 30MeV, strange hadronic matter with the strong YY interaction can not have a bound state. For a neutron star, the mass obtained with the weak YY interaction is consistent with the observations,that with the strong one is inconsistent with the observations, that with no (σ*,φ) mesons included is marginally consistent. This indicates that the inclusion of the(σ*,φ) mesons is essensitial for the study of neutron stars, and the weak YY interaction is more realistic than the other two cases. We find there exists a critical temperature value, higher than which, a stable neutron star can not be formed. This critical temperature value is 40MeV(three cases obtain the same results). We also find that the increase of the temperature can suppress the influence of the strength of the YY interaction on neutron star matter. In protoneutron stars, the weak YY interaction leads to a lower core temperature than the strong one. The neutrino abundance with the weak YY interaction is smaller than that with the strong one. With the weak YY interaction, the mass range of a protoneutron star that will subside into a low mass black is narrowwer than the strong YY interaction.