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Whether fast cooling processes occur or not is crucial for the thermalevolution of neutron stars. In particular, the threshold of the direct Urcaprocess, which is one of the fast cooling processes, is determined by theinterior proton fraction $Y_p$, or the nuclear symmetry energy. Since recentobservations indicate the small radius of neutron stars, a low value ispreferred for the symmetry energy. In this study, simulations of neutron starcooling are performed adopting three models for equation of state (EoS):Togashi, Shen, and LS220 EoSs. The Togashi EoS has been recently constructedwith realistic nuclear potentials under finite temperature, and found toaccount for the small radius of neutron stars. As a result, we find that, sincethe direct Urca process is forbidden, the neutron star cooling is slow with useof the Togashi EoS. This is because symmetry energy of Togashi EoS is lowerthan those of other EoSs. Hence, in order to account for observed age andsurface temperature of isolated neutron stars (INS) with use of the TogashiEoS, other fast cooling processes are needed regardless of the surfacecomposition.

Possibility of rapid neutron star cooling with the realistic equation of state