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COOLING NEUTRON STARS: THEORY AND OBSERVATIONS D.G. Yakovlev Ioffe Physical Technical Institute, St.-Petersburg, Russia Main collaborators: • A.D. Kaminker, Ioffe Institute • A.Y. Potekhin, Ioffe Institute • Introduction • Neutrino emission • Cooling theory • Phenomenological concept • Theory and observation • Connections • Conclusions Hirschegg – January – 2009 Cooling Theory: Primitive and complicated at once Basic Ideas Heat content: UT ~ 1048 T92 ergs PRE-PULSAR HISTORY Stabler (1960) – PhD, First estimates of X-ray surface thermal emission Chiu (1964) – Estimates that neutron stars can be discovered from observations of thermal X-rays Morton (1964) , Chiu & Salpeter (1964), Bahcall & Wolf (1965) – First simplified cooling calculations Tsuruta & Cameron (1966) – Basic formulation of all elements of the cooling theory Neutrino Emission Processes in Neutron Star Cores Direct Urca, N/H n p e e p e n e Pion condensate N N e e N e N e Fast erg cm-3 s-1 Outer core Inner core Slow emission Fast emission } } STANDARD } } } Kaon condensation B B e e B e B e Or quark matter d u e e Modified Urca nN pNe u e d e pNe nN NN bremsstrahlung N N N N Enhanced emission in inner cores of massive neutron stars: Everywhere in neutron star cores: QFAST Q0FT96 LFAST L0FT96 QSLOW Q0ST98 LFAST L0ST98 THREE COOLING STAGES Stage Duration Physics Relaxation 10—100 yr Crust Neutrino 10-100 kyr Core, surface Photon infinite Surface, core, reheating INITIAL THERMAL RELAXATION: LOOK FROM INSIDE AND OUTSIDE OBSERVATIONS AND BASIC COOLING CURVE Nonsuperfluid star Nucleon core EOS PAL (1988) Modified Urca neutrino emission: slow cooling 1=Crab 2=PSR J0205+6449 3=PSR J1119-6127 4=RX J0822-43 5=1E 1207-52 6=PSR J1357-6429 7=RX J0007.0+7303 8=Vela 9=PSR B1706-44 10=PSR J0538+2817 11=PSR B2234+61 12=PSR 0656+14 13=Geminga 14=RX J1856.4-3754 15=PSR 1055-52 16=PSR J2043+2740 17=PSR J0720.4-3125 Talks by Frank Haberl and Slava Zavlin MODIFIED AND DIRECT URCA PROCESSES 1=Crab 2=PSR J0205+6449 3=PSR J1119-6127 4=RX J0822-43 5=1E 1207-52 6=PSR J1357-6429 7=RX J0007.0+7303 8=Vela 9=PSR B1706-44 10=PSR J0538+2817 11=PSR B2234+61 12=PSR 0656+14 13=Geminga 14=RX J1856.4-3754 15=PSR 1055-52 16=PSR J2043+2740 17=PSR J0720.4-3125 M MAX 1.977 M c 2.578 1015 g/cc M D 1.358 M c 8.17 1014 g/cc From 1.1 M to 1.98 M with step M 0.01 M BASIC PHENOMENOLOGICAL CONCEPT Neutrino emissivity function Neutrino luminosity function BASIC PARAMETERS: QSLOW , QFAST , 1 , 2 LSLOW , LFAST , M 1 , M 2 Problems: • To discriminate between neutrino mechanisms • To broaden transition from slow to fast neutrino emission MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION 2p proton SF 1=Crab 2=PSR J0205+6449 3=PSR J1119-6127 4=RX J0822-43 5=1E 1207-52 6=PSR J1357-6429 7=RX J0007.0+7303 8=Vela 9=PSR B1706-44 10=PSR J0538+2817 11=PSR B2234+61 12=PSR 0656+14 13=Geminga 14=RX J1856.4-3754 15=PSR 1055-52 16=PSR J2043+2740 17=PSR J0720.4-3125 M VELA 1.61 M ? MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION -- II 2p proton SF Mass ordering is the same! M VELA 1.47 M ? Neutron stars with strongproton and mild neutron superfluidities in the cores TESTING THE LEVELS OF SLOW AND FAST NEUTRINO EMISSION Slow neutrino emission: Q(Mod Urca) / 30 Fast neutrino emission: Q(Mod Urca) 30 Two other parameters are totally not constrained Broadening of threshold for fast neutrino emission Superfluidity: Suppresses ordinary neutrino processes Initiates Cooper-pairing neutrino emission Should be: Strong in outer core to suppress modified Urca Penetrate into inner core to broaden direct Urca threshold Can be: proton or neutron E.,g. pion polarization Voskresensky &Senatorov (1984, 1986) Schaab et al. (1997) Nuclear physics effects Magnetic broadening Baiko & Yakovlev (1999) Effects of accreted envelopes and surface magnetic fields Different mass M / M of accreted material on the surface Dipole magnetic field in heat blanketing layer Summary of cooling regulators Regulators of neutrino emission in neutron star cores EOS, composition of matter Superfluidity Heat content and conduction in cores Heat capacity Thermal conductivity Thermal conduction in heat blanketing envelopes Thermal conductivity Chemical composition Magnetic field Internal heat sources (for old stars and magnetars) Viscous dissipation of rotational energy Ohmic decay of magnetic fields, ect. CONNECTION: X-ray transients 1 2 3 4 5 6 7 8 9 Direct Urca Aql X-1 4U 1608-522 RX J1709-2639 KS 1731-260 Cen X-4 SAX J1810.8-2609 XTE J2123-058 1H 1905+000 SAX 1808.4-3658 Pion condensate Data collected by Kseniya Levenfish Talk by Rudy Wijnands Kaon condensate CONNECTION: Magnetars Kaminker et al. (2006) SUMMARY OF CONNECTIONS Objects Physics which is tested Middle-aged isolated NSa Neutrino luminosity function Composition and B-field in heat-blanketing envelopes Young isolated NSs Crust Quasistationary XRTs Neutrino luminosity function Composition and B-field in heat-blanketing envelopes Deep crustal heating Quasipersistent XRTs KS 1731—260; MXB 1659—29 Crust Deep crustal heating Superbursts Crust Magnetars after outbursts Crust Magnetars in quasistationary states ?? CONCLUSIONS Today Cooling neutron stars Soft X-ray transients • Constraints on slow and fast neutrino emission levels • Mass ordering Future • New observations and good practical theories of dense matter • Individual sources and statistical analysis CONCLUSIONS Ordinary cooling isolates neutron stars of age 1 kyr—1 Myr • There is one basic phenomenological cooling concept (but many physical realizations) • Main cooling regulator: neutrino luminosity function • Warmest observed stars are low-massive; their neutrino luminosity seems to be <= 1/30 of modified Urca • Coldest observed stars are more massive; their neutrino luminosity should be > 30 of modified Urca (any enhanced neutrino emission would do) • Neutron star masses at which neutrino cooling is enhanced are not constrained • The real physical model of neutron star interior is not selected Connections • Directly related to neutron stars in soft X-ray transients (assuming deep crustal heating). From transient data the neutrino luminosity of massive stars is enhanced by direct Urca or pion condensation • Related to magnetars and superbusrts Future • New observations and accurate theories of dense matter • Individual sources and statistical analysis CONCLUSIONS The case is not solved Plenty of work ahead Neutrino Emission Processes in Neutron Star Cores Enhanced emission in inner cores of massive neutron stars QFAST Q0FT96 Model LFAST L0FT96 Q0 [erg cm 3 s 1 ] Process N/H direct Urca B B e e B e B e 1026 3 1027 Pion condensate N N e e N e N e 1023 1026 Kaon condensate B B e e B e B e 1023 1024 Quark matter d u e e u e d e 1023 1024 Everywhere in neutron star cores QSLOW Q0ST98 LFAST L0ST98 Modified Urca nN pNe pNe nN Bremsstrahlung N N N N 1020 3 1021 1019 1020 Analytical estimates Thermal balance of cooling star with isothermal interior dT C (T ) L (T ) L (Ts ) LHEAT dt L 4 R 2Ts4 L L (1 rg /R ) Heat blanketing envelope: Ts Ts (T ) T (t ) T (r , t ) exp( (r )) Slow cooling via Modified Urca process Fast cooling via Direct Urca process tSLOW 1 year ~ T96 T ~ 1.5 108 K in t 105 yrs tFAST 1 min ~ T94 T ~ 107 K in t 200 yrs MAIN PHYSICAL MODELS Problems: • To discriminate between neutrino mechanisms • To broaden transition from slow to fast neutrino emission Direct Urca Process Lattimer, Pethick, Prakash, Haensel (1991) n p e e , p e n e n n e e p Q 2 wi f f n (1 f p )(1 f e ) d e m 457 2 n m p me 2 Q G (1 3g A ) 10 3 T 6 npe 10080 c Q ~ 3 1027 T96 erg cm3 s 1 46 6 9 L ~ 10 T erg s n 1 e Is forbidden in outer core by momentum conservation: 0 pFn 330 MeV/c, pFe pFp 120 MeV/c, p ~ kBT / c ~ 0.1T9 MeV/c Threshold: pFn pFp pFe ~2 0 Similar processes with muons Similar processes with hyperons, e.g. n In inner cores of massive stars Welcome to the Urca World - I Gamow and Shoenberg: Casino da Urca in Rio de Janeiro Neutrino theory of stellar collapse, Phys. Rev. 59, 539, 1941: Unrecordable cooling agent Photo and Story by R. Ruffini Welcome to the Urca World - II