Exploring interior of neutron star through neutron star cooling I.Introduction II.Thermal evolution of neutron stars -Basic concepts of cooling curve of neutron stars III. Neutrino luminosity as a probe of new form of matter inside neutron stars IV Observation of Cas A and nucleon superfluidity V Summary and concluding remarks T. Tatsumi (Kyoto U.)

I. Introduction crust core Structure of neutron stars

M-R relation (Bulk properties of neutron stars) Cooling curve (Thermal evolution) (Magnetic evolution) EOS (Equation of state) gives Can microphysics understand or explain these observables ? ・ There have been measured various observables about neutron stars, and great progress in observational technique. ・ Unfortunately, most of phenomena occurs near the surface, and can provide us with indirect information about interiors of neutron stars, especially the core region, except their bulk properties. ・ Among them neutron star cooling can give direct information of properties of matter at high densities through neutrino emission.

Magnetars (1985) Dipole radiation

J. Lattimer, arXiv: (P. B. Demorest, Nature 467, 1081, 2010) J. Antoniadis et al. Science 340 (2013) 6131 R.A. Hulse and J.H. Taylor, Ap J. !95(1975) L51.

(P. B. Demorest, Nature 467, 1081, 2010)

D.Page, arXiv: Comparison with observation Crab Cas A 3C 58 Vela Cas A Young pulsars

II. Thermal evolution of neutron stars

(+H)

(crust)

Cold catalyzed matter: ・ chemical equilibrium ・ charge neutrality triangle condition: Ex) n,p,e matter Direct URCA (  decay) cycle is strongly suppressed in normal neutron star matter. e N N Modified URCA For free particles

Neutrino Cooling era: L >> L  Photon Cooling era: L  << L  Basic Cooling: neutrino vs photon cooling eras

No superfluid MURCA (slow cooling) D.G. Yakovlev and C.J. Pethick, Ann. Rev. Astron. Astrophys. 42 (2004) C58 Relaxation Neutrino cooling Photon cooling “Standard” scenario

III. Neutrino luminosity as a probe of new form of matter inside neutron stars Fast cooling Exotic cooling New form of matter Standard cooling Modified URCA+photon (+superfluidity) Slow cooling for 3C58, Vela

New form of matter or Various phases inside neutron stars Strange Quark Matter Boson Condensate Hyperonic Matter Quark Matter K π Σ Λ u d s u d s

Inner cores of massive neutron stars: Nucleons, hyperons Pion condensates Kaon condensates Quark matter Everywhere in neutron star cores. Most important in low-mass stars. Modified Urca process Brems- strahlung

Fast cooling vs slow cooling Exotic cooling – Impact of 3C58 3C58 is the remnant of a supernova observed in the year 1181 by Chinese and Japanese astronomers. A long look by Chandra shows that the central pulsar - a rapidly rotating neutron star formed in the supernova event - is surrounded by a bright torus of X-ray emission. An X-ray jet erupts in both directions from the center of the torus, and extends over a distance of a few light years. Further out, an intricate web of X-ray loops can be seen. (NASA,2004) 3C58

CONCLUSIONS about the THEORY EOS quite well determined The mass of the star has little impact The dominant neutrino emission process is from the formation and breaking of Cooper pairs from the neutron 3P2 gap (unless this gap is very small) Possibility of the presence of light elements in the envelope allows to accommodate a range of T e at a given age S. Tsuruta et al., Ap.J. 571 (2002) L143. e ’’ 

K.G.Elshamouty et al., arXiV: NASA W.C.G. Ho et al, Nature 462 (2009) 71 IV. Observation of Cas A and nucleon superfluidity

D.Page, arXiv: Cas A 3C58

Predictions for the NEUTRON 1 S 0 gap Medium polarization effect O(1/3) Important feature: WE DO NOT REALLY KNOW WHAT IT IS Medium polarization effects were expected to increase the 3 P 2 gap while they probably strongly suppress it.

D. Page et al., astro-ph/ D.G. Yakovlev and C.J. Pethick, Ann. Rev. Astron. Astrophys. 42 (2004) 169. Cooling of compact stars and superfluidity ・ Enhancement of neutrino luminosity ・ Suppression by the pairing New form of matter

Neutrino cooling eraPhoton cooling era

Neutrino emission through the formation and breaking of Cooper pairs (PBF) Flowers, Ruderman & Sutherland, Ap. J. 205 (1976), 541 Voskresenskii & Senatorov, Zh. Eksp. Teor. Fiz. 90 (1986), 1505 [JETP 63 (1986), 885] Voskresenskii & Senatorov, Yad. Fiz. 45 (1987), 657 [Sov. J. Nucl. Phys. 45 (1987), 411] D.G. Yakovlev et al., A&A 343(1999) 650. c.f.Quasiparticle recombination time (life-time) in a superconductor Cooper pairQuasi-particles See also J.R. Schriefer and D.M. Ginsberg, PRL 8 (1962) 207.

Neutral-current weak interaction Emissivity (singlet pairing case) Quasi-particle op. (Flowers, Ruderman & Sutherland, Ap. J. 205 (1976), 541) ex) Singlet pairing

E.Flowers et al.,ApJ 205(1976)541. Emissivity c.f. below T c

Cooper cooling Cooper Pair Neutrino Luminosities vs MURCA and Photons Cas A is around here? Cas A is around here?

D.Page, arXiv: Cas A 3C58

Comments about neutral current processes:

well known unknown Spin content of proton, especially due to ss sea - (T.T., T. Takatsuka, R. Tamagaki, PTP 110 (2003) 179.) ~ 0.3 ~1.47 Ratio of the reaction rate

V Summary and concluding remarks ・ Cooling of neutron stars has provided us with information of high-density matter through the neutrino emission mechanism. ・ Recent observation of Cas A may give information of nucleon superfluidity. ・ Can we catch an evidence about Quark Matter through cooling of “neutron stars”? ・ Simultaneous observation of surface temperature and other observables such as mass, radius … is desired to extract definite conclusions. ・ Surface temperature of some pulsars has already suggested a fast cooling, which may need exotic cooling.

平均場近似と Bogoliubov-Vanatin 変換

Leptonic tensor : ランダウ・リフシッツ 相対論的量子力学

Vector current only :

BCS 理論ミニマム クーパー対の凝縮状態

Lenard integral [A.Lenard (1953), Landau & Lifshitz] For other application, e.g. muon decay :

Neutral current D.G. Yakovlev et al., A&A 343(1999) 650 (Non-rela.) Fermi’s Golden rule :

II. Thermal evolution of neutron stars (I. Sagert et al., arXiv: ) (T. Fischer, CSQCDII)