Cooling of Isolated Neutron Stars with Pion Condensation: Possible Fast Cooling in a Low-Symmetry-Energy Model

We studied thermal evolution of isolated neutron stars (NSs) including the pion condensation core, with an emphasis on the stiffness of equation of state (EOS). Many temperature observations can be explained by the minimal cooling scenario which excludes the fast neutrino cooling process. However, several NSs are cold enough to require it. The most crucial problem for NS cooling theory is whether the nucleon direct Urca (DU) process is open. The DU process is forbidden if the nucleon symmetry energy is significantly low. Hence, another fast cooling process is required in such an EOS. As the candidate to solve this problem, we consider the pion condensation. We show that the low-symmetry-energy model can account for most cooling observations including cold NSs, with strong neutron superfluidity. Simultaneously, it holds the $2~M_{\odot}$ observations even if the pion condensation core exists. Thus, we propose the possibility of pion condensation, as an exotic state to solve the problem in low-symmetry-energy EOSs. We examined the consistency of our EOSs with other various observations as well.