Cooling of Compact Stars with Color Superconducting Quark Matter
Tsuneo Noda, Nobutoshi Yasutake, Masa-aki Hashimoto, Toshiki Maruyama, Toshitaka Tatsumi, Masayuki Y. Fujimoto
aa r X i v : . [ a s t r o - ph . S R ] D ec Cooling of Compact Stars with ColorSuperconducting Quark Matter ∗ Tsuneo Noda † , Nobutoshi Yasutake , Masa-aki Hashimoto ,Toshiki Maruyama , Toshitaka Tatsumi , andMasayuki Y. Fujimoto Kurume Institute of Technology, Fukuoka, 830-0052 JAPAN Physics Department, Chiba Institute of Technology, Chiba,275-0023 JAPAN Department of Physics, Kyushu University, Fukuoka, 812-8581JAPAN Advanced Science Research Center, Japan Atomic Energy Agency,Ibaraki, 319-1195 JAPAN Department of Physics, Kyoto University, Kyoto, 606-8502 JAPAN Department of Physics, Hokkaido University, Sapporo, 060-0810JAPAN
Abstract
We show a scenario for the cooling of compact stars considering the central source ofCassiopeia A (Cas A). The Cas A observation shows that the central source is a compact starwith high effective temperature, and it is consistent with the cooling without exotic phases.The Cas A observation also gives the mass range of M ≥ . M ⊙ . It may conflict with thecurrent cooling scenarios of compact stars that heavy stars show rapid cooling. We includethe effect of the color superconducting (CSC) quark matter phase on the thermal evolutionof compact stars. We assume the gap energy of CSC quark phase is large (∆ & Keywords: dense matter — stars: neutron ∗ Submitted to ACTA ASTRONOMICA SINICA, Proceedings of Quarks and Compact Stars (QCS 2014) † [email protected] Introduction
Cooling theory of compact stars has been dis-cussed for decades. It has been believedthat some compact stars require exotic cool-ing to explain the observations and otherscan be explained by Modified URCA andBremsstrahlung processes (the standard cool-ing). The exotic state appears at high densityregion, and it can be larger than the centraldensity of light compact stars. Therefore, onlyheavy stars have the exotic phase in their coresand they cool faster than lighter stars.The scenario seemed to be fine until the ob-servation of the central source of Cas A [1]. Theobservation of Cas A shows that it is a heavycompact star and its surface temperature is rel-atively high. There were no observation of iso-lated compact star that has the mass and thetemperature together. It satisfies the standardcooling scenario, it seems that all exotic sce-narios ruled out. However, some compact stars(e.g., SAX J1808, 3C38 and Vela pulsar) aredifficult to be explained by the standard sce-narios. It is possible to think these stars havemuch heavier than Cas A, but it may conflictwith current supernovae theory.Recently, the surface temperature of Cas Abecomes an issue. Ref. [2] reported the surfacetemperature of Cas A is decreasing in the past10 years. The temperature drop is too rapid toexplain by usual neutrino emission process, ex-cept superfluidity of neutrons. Recent studies(such as [3–5]) insist that the rapid decrease inthe surface temperature shows that the transi-tion to neutron superfluidity occurs. However,the observation has been re-analyzed [6,7], andthe temperature drop is still under discussion.In this study, we present a model which sat-isfies the temperature-mass relation of Cas Aand the temperatures of other stars, by consid- ering color superconducting (CSC) quark phasein the core of neutron stars.
We construct a model that includes both quark-hadron mixed phase (MP) and CSC phase. Weuse the EoS of the Bruekner-Hartree-Fock the-ory (hadron) and the Dyson-Schwinger theory(quark), including the MP phase between theboth phases [8]. We assume that the entirequark matter (QM) is in the CSC phase withlarge energy gap (∆ &
10 MeV). The max-imum mass with this EoS is 2 . M ⊙ , and itsatisfies the recent 2 M ⊙ observations [9, 10].The EoS of the hadronic phase is stiff enoughto obtain large proton fraction y p . It becomeslarger than the threshold proton fraction of Di-rect URCA process ( y p > / T pCR & × K) works.Another important phase in compact stars isthe neutron P superfluidity. The critical tem-perature of the triplet phase T n3CR is comparablewith the matter temperature during the neu-trino cooling phase. Therefore the transitionto superfluid phase may occur in this duration.The neutron superfluidity has two effects, oneis to suppress the neutrino emissivity in the su-perfluid state, and the other is to emit largenumber of neutrinos at the transition to thesuperfluid state. The emission effect, known as“PBF” (Pair Breaking and Formation), causesrapid drop of the stellar temperature, and it issensitive to the critical temperature. For sim-plicity and the uncertainty of Cas A observa-tion, we do not include the effect of neutronsuperfluidity for our calculation.We select stellar masses of compact stars tobe 1 .
41, 2 .
04, and 2 . M ⊙ . The results areshown in Fig. 1 with available observationalvales (see Ref. [5]). We can see the coolingcurves transit from cooler regions to the hot-ter regions with increasing the mass of com- pact star. It can be said that the compact starwith larger mass cools slower than lighter star.The tendency is opposite to the current coolingscenarios. The cooling curves do not seem tosatisfy the data of 3C58 or Vela pulsar. To ex-plain these observational data, the neutron P t [yr] l og T e ff [ K ] M M M C a s A C V e l a C r ab 1811 − −
52 1706 −
44 1823 − +
61 0656 +
14 0740 − − + Figure 1: Cooling curves with CSC quark phases. Vertical lines indicate the observational data.superfluidity is required for further calculation.
We demonstrate the effect of CSC quark phaseon the cooling curve with the EoS which satis-fies observations of the 2 M ⊙ compact stars. Itis possible to make a situation that heavy starcools slower than lighter stars.To understand the thermal evolution of com-pact stars, considering 3 super phases (neutron P , proton S superfluidity and quark CSC)is important. Quark phase in compact starscan be in CSC phase. Once the CSC phaseappears, it suppress the strong neutrino emis-sion by quarks. In the hadronic phase, neu-tron and proton superfluidity occur at partic-ular density regions. The proton superfluiditysuppresses neutrino emission. The neutron su-perfluidity plays the both roles, rapid coolingduring transition, and suppression to the neu-trino emissivity after the transition. The the-ories of these super phases are still uncertain.Cooling calculation of compact stars can con-nect nuclear theories of high density region andobservations. References [1] W. C. G. Ho & C. O. Heinke, Nature, , 71 (2009).[2] C. O. Heinke & W. C. G. Ho, Astrophys.J. Lett. , L167 (2010).[3] D. G. Yakovlev et al. Mon. Not. R. As-tron. Soc. , 1197 (2011).[4] P. S. Shternin et al. Mon. Not. R. Astron.Soc. , L108 (2011).[5] T. Noda et al. Astrophys. J. , 1(2013).[6] K. G. Elshamouty et al. Astrophys. J. , 22 (2013).[7] B. Posselt et al. Astrophys. J. , 186(2013).[8] N. Yasutake et al. arXiv:1309.1954(2013).[9] P. B. Demorest et al. Nature, , 1081(2010).[10] J. Antoniadis et al. Science,340