Cooling of Compact Stars with Nucleon Superfluidity and Quark Superconductivity

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1 Quark and Compact Stars Feb. Kyoto Univ. Cooling of Compact Stars with Nucleon Superfluidity and Quark Superconductivity Tsuneo NODA ( 野 常雄 ) Kurume Institute of Technology

2 THERMAL HISTORY OF COMPACT STARS Compact stars are born from supernovae explosions. Born at high temperature (~10 10 K) No internal heat source Emitting thermal energy by neutrinos Isolated compact star only cools down. t < 10 5 yr: Neutrino t > 10 5 yr: Photon Compact Star

3 COOLING OF COMPACT STARS The cooling process of compact stars corresponds the internal matter state Normal nuclear matter π condensation K condensation Quark matter Superfluidity etc Exotic phase appears at higher density, and it cools star rapidly. TN+, PoS (NIC-IX) 153, 2006

4 SUPERFLUIDITY Superfluidity has 2 effects Normal Super Transition: ν-emission (PBF/Strong Cooling) After Transition: Suppression of ν-emissivity (Weak Cooling) n- 3 P 2 Density dependence of Critical Temperature Shternin et al. 2011

5 OBSERVATIONS OF COMPACT STARS PSR J and PSR J (Demorest+ 2010, Antoniadis+ 2013) 2M 8 compact stars in binary systems (Companion: WD) The EoS must support the maximum mass 2M 8 Central Source of Cassiopeia A (Cas A) (Ho & Heinke 2009) Isolated compact star Young (~330 yr) & Heavy ( M 8 ) Compact Star, Hot for its age Rapid cooling in these 10 years? (Heinke & Ho 2010, Posselt+ 2013) PSR J (3C58) (Slane+ 2002), Vela Pulsar (Pavlov+ 2001) Isolated compact stars Cold for their ages, mass unknown SAX J (Campana+ 2002) Compact star in LMXB Lower surface temperature for accretion rate Exotic cooling process required

6 MOTIVATION Cassiopaia A Hot, young and heavy Isolated compact star with known mass range 3C58 / Vela Cold compact stars Older than Cas A Lower temperature Isolated compact stars (mass range unknown) Should be explained by a single model! Cas A is heavy, and has an exotic phase, but not cooled down Colour Superconductivity in quark phase (TN+,2013)

7 MODELS Hybrid Star EoS Satisfied 2M 8 Brueckner-Hartree-Fock (HM) + Dyson-Schwinger (QM) Mixed phase between HM-QM (Yasutake+ 2016) Cooling Process Modified URCA + Bremsstrahlung n-super( 1 S 0, 3 P 2 ), p-super( 1 S 0 ) Direct URCA (y e >1/9) Quark Cooling with Colour Superconductivity (CFL) Parameters Mass Critical Teperature model of nucleon superfluidity Mass [M 8 ] Quark Mixed J J Cas A 1.41M Radius [km]

8 Quark matter at high density Colour super conductivity (CSC) Assuming CFL paring CSC state has similar effect to nucleon superfluidity Δ 10 MeV Suppression of neutrino emissivity exp(-δ/k B T) p F QUARK PHASE Unpaired 2SC Pairing CFL Pairing R G B d u s p F R G B d u s p F R G B d u s Between hadronic phase Quark Hadron Mixed Phase No uniform QM appears in this model

9 COOLING PROCESSES Hadronic Phase Bremsstrahlung Modified URCA PBF (Superfluid) Direct URCA Quark Phase Quark β-decay with n/p-super with n/p-super with n/p-super (y p > 1/9) with Q-super (CFL Phase, Δ 10 MeV) Density

10 NUCLEON SUPERFLUIDITY (SIMPLE MODEL) n, p superfluidity Neutron: 1 S 0, 3 P 2 Proton: 1 S Critical Temperature (T cr ) Parameterized density dependence Effects for Cooling On Transition: Strong cooling (Pair Breaking and Formation) (Page+ 2004) After transition: Suppress other neutrino emissivities T cr [K] n 1 S 0 p 1 S 0 ρ [g cm 3 ] n 3 P 2

11 RESULTS (SIMPLE MODEL) Cas A p 1 S 0 n 1 S 0 n 3 P 2 T cr [K] C58 Vela ρ [g cm 3 ] Changing n- 3 P 2 model Large T CR Lighter star cools faster Small T CR Heavier star cools faster

12 RESULTS (SIMPLE MODEL) Cas A p 1 S 0 n 1 S 0 T cr [K] 10 9 n 3 P 2 3C58 10 Vela ρ [g cm 3 ] Changing p- 1 S 0 model Cooling pattern changed, Not large effect, compared with n- 3 P 2

13 PROBLEMS OF THE SIMPLE MODEL Conflict with nuclear theory No match with EoS M M M 8 p 1 S 0 T cr [K] 10 9 n 1 S 0 Takatsuka & Tamagaki n 3 P ρ [g cm 3 ]

14 RESULTS (MODIFIED MODEL) M M M 8 p 1 S 0 T cr [K] 10 9 n 1 S 0 n 3 P ρ [g cm 3 ] Mid-mass compact star remains warm Heavy star cools faster

15 SUMMARY Cooling curves of compact stars with changing superfluidity models Mass-Temperature relation: Depending on Superfluid Model Temperature-mass relation of Cas A can be explained Direct URCA process is too strong No strong constraints for quark matter 3 Super States are important for Compact Star Cooling Neutron Superfluidity Large T cr transition at early phase Suppression of other ν Marginal T cr transition in cooling period Strong Cooling Proton Superfluidity Marginal T cr Suppression of Direct URCA Quark CSC Large Δ Suppression of Strong Quark cooling

16 FUTURE PROSPECTS Superfluid model should match with the EoS Other exotic states, CSC paring Hyperon-mixed, Meson-condensation 2SC paring Direct URCA problem To satisfy 2M 8 compact stars Stiff hadronic EoS Proton fraction can exceed 1/9 Direct URCA works in the core