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THERMAL EVOLUTION OF NEUTRON STARS: Theory and observations 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 Catania, October 2012, THREE COOLING STAGES After 1 minute of proto-neutron star stage 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 dTi C (Ti ) L (Ti ) L (Ts ) dt L 4 R 2Ts4 L L (1 rg /R ) Heat blanketing envelope: Ts Ts (T ) Ti (t ) T ( r, t ) exp(( r )) Slow cooling via Modified Urca process Fast cooling via Direct Urca process tSLOW 1 year ~ Ti 69 Ti ~ 1.5 108 K in t 105 yrs tFAST 1 min ~ Ti 94 Ti ~ 107 K in t 200 yrs Spin axis OBSERVATIONS: MAIN PRINCIPLES 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 Minimal cooling; SF off – does not explain all data MAXIMAL COOLING; SF OFF 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 Does not explain the data 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 MAXIMAL COOLING: SRTONG PROTON SF 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”) MAXIMAL COOLING: SRTONG PROTON SF M VELA 1.61 M ? MAXIMAL COOLING: STRONG PROTON SF – II Mass ordering is the same! M VELA 1.47 M ? MINIMUM AND MAXIMUM COOLING SF on Gusakov et al. (2004, 2005) Minimum cooling Gusakov et al. (2004) Minimum-maximum cooling Gusakov et al. (2005) Cassiopeia A supernova remnant Very bright radio source Weak in optics due to interstellar absoprtion Distance: kpc (Reed et al. 1995) Diameter: 3.1 pc No historical data on progenitor Asymmetric envelope expansion Age yrs => 1680 from observations of expanding envelope (Fesen et al. 2006) Cassiopeia A observed by the Hubble Space Telescope MYSTERIOUS COMPACT CENTRAL OBJECT IN Cas A SNR Various theoretical predictions: e.g., a black hole (Shklovsky 1979) Discovery: Tananbaum (1999) first-light Chandra X-ray observations Later found in ROSAT and Einstein archives Later studies (2000-2009): Pavlov et al. (2000) Chakrabarty et al. (2001) Pavlov and Luna (2009) Main features: 1. No evidence of pulsations 2. Spectral fits using black-body model or He, H, Fe atmosphere models give too small radius R<5 km Conclusion: MYSTERY – Not a thermal X-ray radiation emitted from the entire surface of neutron star A Chandra X-ray Observatory image of the supernova remnant Cassiopeia A. Credit: Chandra image: NASA/CXC/Southampton/W.Ho; illustration: NASA/CXC/M.Weiss COOLING NEUTRON STAR IN Cas A SNR Ho and Heinke (2009) Nature 462, 671 Fitting the observed spectrum with carbon atmosphere model gives the emission from the entire neutron star surface Conclusion: Cas A SNR contains cooling neutron star with carbon surface It is the youngest cooling NS whose thermal radiation is observed Neutron star parameters Main features: 1. Rather warm neutron star 2. Consistent with standard cooling 3. Not interesting for cooling theory!!! (Yakovlev et al. 2011) OBSERVATIONS available for Ho and Heinke (2009) Heinke and Ho (2010): 16 sets of Chandra observations in 2000, 2002, 2004, 2006, 2007, 2009 totaling 1 megasecond (two weeks) REVOLUTION: Cooling Dynamics of Cas A NS! Heinke & Ho, ApJL (2010): Surface temperature decline by 4% over 10 years “Standard cooling” cannot explain these observations Observed cooling curve slope Ho & Heinke 2010 New observation Standard cooling M, R, d, NH are fixed Cas A neutron star: 1. Is warm as for standard cooling 2. Cools much faster than for standard cooling s Standard cooling curve slope d ln Ts 1.35 0.15 (2 ) d ln t s d ln Ts 0.1 d ln t Effects of Superfluidity on Cooling Neutron superfluidity: Faster cooling because of CP neutrino emission Proton superfluidity: Slower cooling because of suppression of neutrino emission Together: Sharp acceleration of cooling Superfluidity naturally explains observations! Both, neutron and proton, superfluids are needed Superfluidity Strong proton Moderate neutron Tc – profile >3x109 K, profile unimportant maximum: TCn(max)~(5-9)x108 K and wide Tc –profile over NS core Appears Early a few decays ago What for? suppresses neutrino emission before the appearance of neutron superfluidity produces neutrino outburst Example: Cooling of 1.65 Msun Star APR EOS Neutrino emission peak: ~80 yrs ago Neutron stars of different masses Cas A neutron star among other isolated neutron stars One model of superfluidity for all neutron stars Only Tcn superfluidity I explains all the sources Gusakov et al. (2004) Alternatively: wider profile, but the efficiency of CP neutrino emission at low densities is weak Slope of cooling curve Measure Ts (t )~t s { d log Ts infer s d log t = slope of cooling curve s 1 / 12 = standard cooling (Murca) s 1 / 8 = enhanced cooling (Durca) s >> 0.1 => something extraordinary! Theoretical model for Cas A NS Shternin et al. (2011) Now: s = 1.35 = very big number => unique phenomenon! Happens very rarely! Measurements of s in the next decade confirm or reject this interpretation Cooling objects – connections • Isolated (cooling) neutron stars • Accreting neutron stars in X-ray transients (heated inside) • Sources of superbursts • Magnetars (heated inside) INSs Cooling of initially hot star XRTs Deep crustal heating: Theory: Haensel & Zdunik (1990) Applications to XRTs: Brown, Bildsten & Rutledge (1998) Magnetars Magnetic heating CONCLUSIONS (without Cas A) OBSERVATIONS •Include sources of different types •Seem more important than theory •Are still insufficient to solve NS problem THEORY •Too many successful explanations • Main cooling regulator: neutrino luminosity • Warmest observed stars are low-massive; their neutrino luminosity <= 0.01 of modified Urca • Coldest observed stars are more massive; their neutrino luminosity >= 100 of modified Urca CONCLUSIONS about Cas A • Observations of cooling Cas A NS in real time – matter of good luck! • Natural explanation: onset of neutron superfluidity in NS core about 80 years ago; maximum Tcn in the core >~7 x 108 K • Profile of critical temperature of neutrons over NS core should be wide • Neutrino emission prior to onset of neutron superfluidity should be 20-100 times smaller than standard level strong proton superfluidity in NS core? • To explain all observations of cooling NSs by one model of superfluidity, Tcn profile has to be shifted to higher densities • Prediction: fast cooling will last for a few decades • Cooling of Cas A NS direct evidence for superfluidity? Two Cas A teams Minimal cooling theory: Page, Lattimer, Prakash, Steiner (2004) Gusakov, Kaminker, Yakovlev, Gnedin (2004) Superfluid Cas A neutron star: D. Page, M. Prakash, J.M. Lattimer, A.W. Steiner, PRL, vol. 106, Issue 8, id. 081101 (2011) P.S. Shternin, D.G. Yakovlev, C.O. Heinke, W.C.G. Ho, D.J. Patnaude, MNRAS Lett., 412, L108 (2011) Doubts Carbon atmosphere: why? Theory: probability to observe is small (too good to be true) Theory: to explain observations of all cooling neutron stars one needs unusual Tcn – profile over neutron star core Observations: data processing???