Cooling of Hybrid Stars with a 2SC+〈 <i>dd</i> 〉 Phase

Abstract Recently, Fujimoto, Fukushima, &amp; Weise (2019) have proposed a new color-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 3P2 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 3P2 superfluidity plays an important role in cooling curves with not the 2SC but 2SC+〈dd〉 phases due to the suppression of quark β 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.