Cooling of Hybrid Stars with a 2SC+$<dd>$ Phase

Recently, Fujimoto, Fukushima & Weise (2019) have proposed a new colour-superconductive state, 2SC+$<dd>$ phase, which can be smoothly connected to the low-density baryon superfluidity in contrast to the 2SC phase. In this scenario, the neutron ${}^3P_2$ superfluidity on the low-density side of the phase transition is inherited by unpaired $d$-quarks in the 2SC phase on the high-density side. Since this could be realized in hybrid stars (neutron stars containing hadronic and quark matter), the 2SC+$<dd>$ phase may change the properties of neutron stars compared to the traditional 2SC phase. In this work, we study the thermal evolution of hybrid stars with the 2SC+$<dd>$ phase for the first time. We find that NSs with the 2SC+$<dd>$ phase become hotter than those with the 2SC phase, and are close to the CFL phase. The ${}^{3}P_2$ superfluidity plays an important role in cooling curves with not the 2SC but 2SC+$<dd>$ phases due to the suppression of quark $\beta$ decay. We therefore point out that, if the scenario of 2SC+$<dd>$ phase is true, it could be specified through low-temperature observations such as Vela, 3C58, Vela Jr., and Vela-like pulsar.