We present a new scenario for the cooling of compact stars considering the central source of Cassiopeia A (Cas A). The Cas A observation shows that the central source is a compact star that has high effective temperature, and it is consistent with the cooling without exotic phases. The observation also gives the mass range of M 1.5M ⊙ , which may conflict with the current plausible cooling scenario of compact stars. There are some cooled compact stars such as Vela or 3C58, which can be barely explained by the minimal cooling scenario, which includes the neutrino emission by nucleon superfluidity (PBF). Therefore, we invoke the exotic cooling processes, where a heavier star cools faster than lighter one. However, the scenario seems to be inconsistent with the observation of Cas A. Therefore, we present a new cooling scenario to explain the observation of Cas A by constructing models that include a quark color superconducting (CSC) phase with a large energy gap; this phase appears at ultrahigh density region and reduces neutrino emissivity. In our model, a compact star has CSC quark core with a low neutrino emissivity surrounded by high emissivity region made by normal quarks. We present cooling curves obtained from the evolutionary calculations of compact stars: while heavier stars cool slowly, and lighter ones indicate the opposite tendency without considering nucleon superfluidity. Furthermore, we show that our scenario is consistent with the recent observations of the effective temperature of Cas A during the last 10 years, including nucleon superfluidity.

Type I X-ray bursts are thermonuclear explosions on the neutron star (NS) surface caused by mass accretion from a companion star. Observations of X-ray bursts provide valuable information on X-ray binary systems, e.g., binary parameters, the chemical composition of accreted matter, and the nuclear equation of state (EOS). There have been several theoretical studies to constrain the physics of X-ray bursters. However, they have mainly focused on the burning layers above the solid crust of the NS, which brings up issues of the treatment of NS gravitational and internal energy. In this study, focusing on the microphysics inside NSs, we calculate a series of X-ray bursts using a general-relativistic stellar-evolution code with several NS EOSs. We compare the X-ray-burst models with the burst parameters of a clocked burster associated with GS 1826–24. We find a monotonic correlation between the NS radius and the light-curve profile. A larger radius shows a higher recurrence time and a large peak luminosity. In contrast, the dependence of light curves on the NS mass becomes more complicated, where neutrino cooling suppresses the efficiency of nuclear ignition. We also constrain the EOS and mass of GS 1826–24, i.e., stiffer EOSs, corresponding to larger NS radii, are not preferred due to a too-high peak luminosity. The EOS and the cooling and heating of NSs are important to discuss the theoretical and observational properties of X-ray bursts.

Quiescent X-ray luminosities are presented in low mass X-ray binaries with use of evolutionary calculations. The calculated luminosities are compared with observed ones in terms of timeaveraged mass accretion rate. It is shown that neutrino emission by strong pion condensation can explain quiescent X-ray luminosity of SAX J1808.4-3658 and we do not need direct Urca processes concerning nucleons and/or hyperons.

Whether fast cooling processes occur or not is crucial for the thermal evolution of neutron stars. In particular, the threshold of the direct Urca process, which is one of the fast cooling processes, is determined by the interior proton fraction $Y_p$, or the nuclear symmetry energy. Since recent observations indicate the small radius of neutron stars, a low value is preferred for the symmetry energy. In this study, simulations of neutron star cooling are performed adopting three models for the equation of state (EoS): Togashi, Shen, and LS220 EoSs. The Togashi EoS has been recently constructed with realistic nuclear potentials under finite temperature, and found to account for the small radius of neutron stars. As a result, we find that, since the direct Urca process is forbidden, the neutron star cooling is slow with use of the Togashi EoS. This is because the symmetry energy of Togashi EoS is lower than those of other EoSs. Hence, in order to account for observed age and surface temperature of isolated neutron stars with the use of the Togashi EoS, other fast cooling processes are needed regardless of the surface composition.

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