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COOLING OF NEUTRON STARS D.G. Yakovlev Ioffe Physical Technical Institute, St.-Petersburg, Russia 1. Formulation of the Cooling Problem 2. Superlfuidity and Heat Capacity 3. Neutrino Emission 4. Cooling Theory versus Observations • History • Cooling stages • Observations • Tuning theory to explain observations • Conclusions Ladek Zdroj, February 2008, 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 NEW HISTORY Lattimer, Pethick, Prakash & Haensel (1991) The possibility of direct Urca process in nucleon matter Page & Applegate (1992) Crucial importance of superfluidity for cooling Schaab, Voskresensky, Sedrakian, Weber & Weigel (1997); Page (1998) The importance of Cooper pairing neutrino emission THREE COOLING STAGES After 1 minute of proto-neutron star stage of Sanjay Reddy Stage Duration Physics Relaxation 10—100 yr Crust Neutrino 10-100 kyr Core, surface Photon infinite Surface, core, reheating 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 Spin axis OBSERVATIONS: MAIN PRINCIPLES See lectures by Roberto Turolla Isolated (cooling) neutron stars – no additional heat sources: Age t Surface temperature Ts MEASURING DISTANCES: parallax; electron column density from radio data; association with clusters and supernova remnants; fitting observed spectra MEASURING AGES: pulsar spin-down age (from P and dP/dt); association with stellar clusters and supernova remnants MEASURING SURFACE TEMPERATURES: fitting observed spectra OBSERVATIONS Chandra image of the Vela pulsar wind nebula NASA/PSU Pavlov et al Chandra XMM-Newton MULTIWAVELENGTH SPECTRUM OF THE VELA PULSAR t (1.1 2.5) 104 yr TS 0.65 0.71 MK THERMAL RADIATION FROM ISOLATED NEUTRON STARS OBSERVATIONS AND BASIC COOLING CURVE Nonsuperfluid star Nucleon core 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 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 MAIN PHYSICAL MODELS Problems: To discriminate between neutrino mechanisms To broaden transition from slow to fast neutrino emission AN EXAMPLE OF SUPERFLUID BROADENING OF DIRECT URCA THRESHOLD Two models for proton superfluidity Neutrino emissivity profiles Superfluidity: • Suppresses modified Urca process in the outer core • Suppresses direct Urca just after its threshold (“broadens the threshold”) BASIC PHENOMENOLOGICAL CONCEPT Neutrino emissivity function Neutrino luminosity function BASIC PARAMETERS: QSLOW , QFAST , 1 , 2 LSLOW , LFAST , M 1 , M 2 MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION M VELA 1.61 M ? MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION -- II Mass ordering is the same! M VELA 1.47 M ? 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 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: Soft X-ray transients Deep crustal heating: Brown, Bildsten, Rutledge (1998) Energy release: Haensel & Zdunik (1990,2003), Gupta et al. (2007) Levenfish, Haensel (2007) SAX J1808.4-3658, talk by Craig Heinke More in the next talk by Peter Jonker CONNECTION: Magnetars Kaminker et al. (2006) SUMMARY OF CONNECTIONS Sources: X-ray transients; magnetars; superbursts Processes: quasistationary and transient 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 should 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 REFERENCES C.J. Pethick. Cooling of neutron stars. Rev. Mod. Phys. 64, 1133, 1992. D.G. Yakovlev, C.J. Pethick. Neutron Star Cooling. Annu. Rev. Astron. Astrophys. 42, 169, 2004. D. Page, U. Geppert, F. Weber. The cooling of compact stars. Nucl. Phys. A 777, 497, 2006.