1. COOLING OF NEUTRON STARS D.G. Yakovlev Ioffe Physical Technical Institute, St.-Petersburg, Russia Ladek Zdroj, February 2008, 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

2. 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

3. 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

4. StageDurationPhysics Relaxation10—100 yrCrust Neutrino10-100 kyrCore, surface PhotoninfiniteSurface, core, reheating THREE COOLING STAGES After 1 minute of proto-neutron star stage of Sanjay Reddy

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

6. 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 See lectures by Roberto Turolla

7. OBSERVATIONS Chandra image of the Vela pulsar wind nebula NASA/PSU Pavlov et al ChandraXMM-Newton

8. MULTIWAVELENGTH SPECTRUM OF THE VELA PULSAR

9. THERMAL RADIATION FROM ISOLATED NEUTRON STARS

10. 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

11. 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

12. MAIN PHYSICAL MODELS Problems: To discriminate between neutrino mechanisms To broaden transition from slow to fast neutrino emission

13. AN EXAMPLE OF SUPERFLUID BROADENING OF DIRECT URCA THRESHOLD 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”)

14. BASIC PHENOMENOLOGICAL CONCEPT Neutrino emissivity functionNeutrino luminosity function

15. MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION

16. MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION -- II Mass ordering is the same!

17. TESTING THE LEVELS OF SLOW AND FAST NEUTRINO EMISSION Slow neutrino emission: Fast neutrino emission: Two other parameters are totally not constrained

18. 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.

19. Levenfish, Haensel (2007) CONNECTION: Soft X-ray transients Deep crustal heating: Brown, Bildsten, Rutledge (1998) Energy release: Haensel & Zdunik (1990,2003), Gupta et al. (2007) SAX J1808.4-3658, talk by Craig Heinke More in the next talk by Peter Jonker

20. CONNECTION: Magnetars Kaminker et al. (2006) SUMMARY OF CONNECTIONS Sources: X-ray transients; magnetars; superbursts Processes: quasistationary and transient

21. CONCLUSIONS Future Today New observations and good practical theories of dense matter Individual sources and statistical analysis Cooling neutron starsSoft X-ray transients Constraints on slow and fast neutrino emission levels Mass ordering

22. 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

23. 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. REFERENCES