THERMAL EVOLUTION OF NEUTRON STARS: Theory and observations D.G. Yakovlev Ioffe Physical Technical Institute, St.-Petersburg, Russia Catania, October 2012, 1. Formulation of the Cooling Problem 2. Superlfuidity and Heat Capacity 3. Neutrino Emission 4. Cooling Theory versus Observations

StageDurationPhysics Relaxation10—100 yrCrust Neutrino kyrCore, surface PhotoninfiniteSurface, core, reheating THREE COOLING STAGES After 1 minute of proto-neutron star stage

Analytical estimates Thermal balance of cooling star with isothermal interior Slow cooling via Modified Urca process Fast cooling via Direct Urca process

OBSERVATIONS: MAIN PRINCIPLES Spin axis B- axis Isolated (cooling) neutron stars – no additional heat sources: Age t Surface temperature T s 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 ChandraXMM-Newton

MULTIWAVELENGTH SPECTRUM OF THE VELA PULSAR

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 J =PSR J =RX J =1E =PSR J =RX J =Vela 9=PSR B =PSR J =PSR B =PSR =Geminga 14=RX J =PSR =PSR J =PSR J Does not explain the data

MAXIMAL COOLING: SRTONG PROTON SF Two models for proton superfluidityNeutrino 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

MAXIMAL COOLING: STRONG PROTON SF – II Mass ordering is the same!

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 Cassiopeia A observed by the Hubble Space Telescope 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)

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 ( ): 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 Neutron star parameters 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) Conclusion: Cas A SNR contains cooling neutron star with carbon surface It is the youngest cooling NS whose thermal radiation is observed Main features: 1.Rather warm neutron star 2.Consistent with standard cooling 3.Not interesting for cooling theory!!! (Yakovlev et al. 2011)

Heinke & Ho, ApJL (2010): Surface temperature decline by 4% over 10 years Ho & Heinke 2010 New observation Standard cooling “Standard cooling” cannot explain these observations M, R, d, N H are fixed Observed cooling curve slope REVOLUTION: Cooling Dynamics of Cas A NS! Cas A neutron star: 1.Is warm as for standard cooling 2.Cools much faster than for standard cooling Standard cooling curve slope

Neutron superfluidity: Proton superfluidity: Together: Faster cooling because of CP neutrino emission Slower cooling because of suppression of neutrino emission Sharp acceleration of cooling Effects of Superfluidity on Cooling Superfluidity naturally explains observations! Both, neutron and proton, superfluids are needed SuperfluidityStrong protonModerate neutron T c – profile>3x10 9 K, profile unimportant maximum: T Cn (max)~(5-9)x10 8 K and wide T c –profile over NS core AppearsEarlya 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

Only T cn superfluidity I explains all the sources One model of superfluidity for all neutron stars Alternatively: wider profile, but the efficiency of CP neutrino emission at low densities is weak Gusakov et al. (2004) Cas A neutron star among other isolated neutron stars

Slope of cooling curve = standard cooling (Murca) = slope of cooling curve = enhanced cooling (Durca) >> 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) Deep crustal heating: Theory: Haensel & Zdunik (1990) Applications to XRTs: Brown, Bildsten & Rutledge (1998) INSsXRTs Magnetars Magnetic heating Cooling of initially hot star

CONCLUSIONS (without Cas A) 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 OBSERVATIONS Include sources of different types Seem more important than theory Are still insufficient to solve NS problem

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 T cn in the core >~7 x 10 8 K Profile of critical temperature of neutrons over NS core should be wide Neutrino emission prior to onset of neutron superfluidity should be times smaller than standard level  strong proton superfluidity in NS core? To explain all observations of cooling NSs by one model of superfluidity, T cn 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 (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 T cn – profile over neutron star core Observations: data processing???