2. Neutron Stars 3: Thermal evolution Andreas Reisenegger Depto. de Astronomía y Astrofísica Pontificia Universidad Católica de Chile

3. Outline Cooling processes of NSs: –Neutrinos: direct vs. modified Urca processes, effects of superfluidity & exotic particles –Photons: interior vs. surface temperature Cooling history: theory & observational constraints Accretion-heated NSs in quiescence Late reheating processes: –Rotochemical heating –Gravitochemical heating & constraint on dG/dt –Superfluid vortex friction –Crust cracking

4. Bibliography Yakovlev et al. (2001), Neutrino Emission from Neutron Stars, Physics Reports, 354, 1 (astro-ph/0012122) Shapiro & Teukolsky (1983), Black Holes, White Dwarfs, & Neutron Stars, chapter 11: Cooling of neutron stars (written before any detections of cooling neutron stars) Yakovlev & Pethick (2004), Neutron Star Cooling, Ann. Rev. A&A, 42, 169

5. General ideas Neutron stars are born hot (violent core collapse) They cool through the emission of neutrinos from their interior & photons from their surface Storage, transport, and emission of heat depend on uncertain properties of dense matter (strong interactions, exotic particles, superfluidity) Measurement of NS surface temperatures (and ages or accretion rates) can allow to constrain these properties Very old NSs may not be completely cold, due to various proposed heating mechanisms These can also be used to constrain dense-matter & gravitational physics.

6. “Urca processes” NS cooling through emission of neutrinos & antineutrinos Direct Urca: –Rates depend on available initial & final states Much slower than free n decay because of Pauli Still very fast on astrophysical scales –Require high fraction of protons & electrons for momentum conservation: possibly forbidden Modified Urca: –Rates reduced because additional particle must be present at the right time, but always allowed Why Urca: These processes make stars lose energy as quickly as George Gamow lost his money in the “Casino da Urca” in Brazil...

7. Surface temperature Model for heat conduction through NS envelope (Gudmundsson et al. 1983) Potekhin et al. 1997

8. Cooling (& heating) Heat capacity of non-interacting, degenerate fermions C  T (elementary statistical mechanics) –Can also be reduced through Cooper pairing: will be dominated by non- superfluid particle species Cooling & heating don’t affect the structure of the star (to a very good approximation)

9. Observations Thermal X-rays are: faint absorbed by interstellar HI often overwhelmed by non-thermal emission difficult to detect & measure precisely D. J. Thompson, astro-ph/0312272

10. Cooling with modified Urca & no superfluidity vs. observations

11. Direct vs. modified Urca Yakovlev & Pethick 2004

12. Effect of exotic particles Yakovlev & Pethick 2004

13. Superfluid games - 1 Yakovlev & Pethick 2004

14. Superfluid games - 2 Yakovlev & Pethick 2004

15. Heating neutron star matter by weak interactions Chemical (“beta”) equilibrium sets relative number densities of particles (n, p, e,...) at different pressures Compressing a fluid element perturbs equilibrium Non-equilibrium reactions tend to restore equilibrium “Chemical” energy released as neutrinos & “heat” Reisenegger 1995, ApJ, 442, 749

16. Possible forcing mechanisms Neutron star oscillations (bulk viscosity): SGR flare oscillations, r-modes – Not promising Accretion: effect overwhelmed by external & crustal heat release – No. d  /dt: “Rotochemical heating” – Yes dG/dt: “Gravitochemical heating” - !!!???

17. “Rotochemical heating” NS spin-down (decreasing centrifugal support)  progressive density increase  chemical imbalance  non-equilibrium reactions  internal heating  possibly detectable thermal emission Idea & order-of-magnitude calculations: Reisenegger 1995 Detailed model: Fernández & Reisenegger 2005, ApJ, 625, 291

18. Yakovlev & Pethick 2004 Recall standard neutron star cooling: No thermal emission after 10 Myr.

19. Thermo-chemical evolution Variables: Chemical imbalances Internal temperature T Both are uniform in diffusive equilibrium.

20. MSP evolution Magnetic dipole spin-down (n=3) with P 0 = 1 ms; B = 10 8 G; modified Urca Internal temperature Chemical imbalances Stationary state Fernández & R. 2005

21. Insensitivity to initial temperature Fernández & R. 2005 For a given NS model, MSP temperatures can be predicted uniquely from the measured spin-down rate.

22. PSR J0437-4715: the nearest millisecond pulsar

23. SED for PSR J0437-4715 HST-STIS far-UV observation (1150-1700 Å) Kargaltsev, Pavlov, & Romani 2004

24. PSR J0437-4715: Predictions vs. observation Fernández & R. 2005 Observational constraints Theoretical models Direct Urca Modified Urca

25. Old, classical pulsars: sensitivity to initial rotation rate D. González, in preparation

26. dG/dt ? Dirac (1937): constants of nature may depend on cosmological time. Extensions to GR (Brans & Dicke 1961) supported by string theory Present cosmology: excellent fits, dark mysteries, speculations: “Brane worlds”, curled-up extra dimensions, effective gravitational constant Observational claims for variations of – (Webb et al. 2001; disputed) – (Reinhold et al. 2006)  See how NSs constrain d/dt of

27. Gravitochemical heating dG/dt (increasing/decreasing gravity)  density increase/decrease  chemical imbalance  non-equilibrium reactions  internal heating  possibly detectable thermal emission Jofré, Reisenegger, & Fernández 2006, Phys. Rev. Lett., 97, 131102

28. Most general constraint from PSR J0437-4715 PSR J0437-4715 Kargaltsev et al. 2004 obs. “Modified Urca” reactions (slow ) “Direct Urca” reactions (fast)

29. Constraint from PSR J0437-4715 assuming only modified Urca is allowed PSR J0437-4715 Kargaltsev et al. 2004 obs. Modified Urca Direct Urca

30. Main uncertainties Atmospheric model: –Deviations from blackbody H atmosphere underpredicts Rayleigh-Jeans tail B. Droguett Neutrino emission mechanism/rate: –Slow (mod. Urca) vs. fast (direct Urca, others) –Cooper pairing (superfluidity): Reisenegger 1997; Villain & Haensel 2005 C. Petrovich, N. González –Phase transitions: I. Araya Not important (because stationary state): –Heat capacity –Heat transport through crust

31. Other heating mechanisms Accretion of interstellar gas –Only for slowly moving, slowly rotating and/or unmagnetized stars –Does not seem to be enough to make old NSs observable (conclusion of Astro. Estelar Avanzada 2008-2) Vortex friction (Shibazaki & Lamb 1989, ApJ, 346, 808) –Very uncertain parameters –More important for slower pulsars with higher B: Crust cracking (Cheng et al. 1992, ApJ, 396, 135 - corrected by Schaab et al. 1999, A&A, 346, 465) –Similar dependence as rotochemical; much weaker