2. Neutron Stars 3: Thermal evolution Andreas Reisenegger ESO Visiting Scientist Associate Professor, 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. Neutron decay (again!): (excerpts from Yakovlev et al. 2001)

7. Dense matter Equilibrium: Fermi sphere: Non-interacting particles (not a great approx.): Charge neutrality: Relevant regime: Combining: Relativistic limit:

8. Direct Urca processes n, p, e all have degenerate Fermi-Dirac distributions (kT << E F   )  Reactants & products must be within  kT of their Fermi energies  Emitted neutrinos & antineutrinos must have energies ~kT Why Urca: These processes make stars lose energy as quickly as George Gamow lost his money in the “Casino da Urca” in Brazil... Fermi-Dirac distribution function (expected # of fermions per orbital) for T = 0 and 0 < kT << E F  

9. Direct Urca rates (excerpts from Yakovlev et al. 2001) Energy/time/volume emitted as

10. Momentum conservation?

11. Modified Urca processes Let an additional nucleon N (=n or p) participate in the reaction, without changing its identity, but exchanging momentum with the reacting particles: In this case, momentum conservation can always be satisfied.

12. Modified Urca rates cf. direct Urca: (excerpts from Yakovlev et al. 2001)

13. Exotic particles At high densities, exotic particles such as mesons or even “free” quarks may be present These generally allow for variants of the direct Urca processes, nearly as fast

14. Superfluid reduction factor “Cooper pairing” of nucleons (n or p or both) creates a gap in the available states around the Fermi energy, generally reducing the reaction rates. Yakovlev et al. 2001

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

16. 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)

17. 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

18. Yakovlev & Pethick 2004

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

21. Direct vs. modified Urca Yakovlev & Pethick 2004

22. Effect of exotic particles Yakovlev & Pethick 2004

23. Superfluid games - 1 Yakovlev & Pethick 2004

24. Superfluid games - 2 Yakovlev & Pethick 2004

25. Soft X-ray transients - 1 Binary systems with episodic accretion Material falls onto the NS surface & undergoes several nuclear transformations: H  He  C  heavier elements Most of the energy gets emitted quickly, near the surface of the star, but ~1MeV/nucleon is released deep in the crust This energy (  accreted mass) heats the neutron star interior, and is released over ~10 6 yr as neutrinos from the interior & quiescent X-rays from the surface

26. Soft X-ray transients - 2 Accretion rate vs. quiescent X-ray luminosity: predictions & observations. Problem: Observe accretion rate only over a few years, need average over millions of years. Yakovlev & Pethick 2004

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

28. 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” - !!!???

29. “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

30. Yakovlev & Pethick 2004 Recall standard neutron star cooling: 1) No thermal emission after 10 Myr. 2) Finite diffusion time matters only during first few 100 yr. 3) Cooling of young neutron stars in rough agreement with slow cooling models (modified Urca)

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

32. 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

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

34. PSR J0437-4715: the nearest millisecond pulsar

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

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

37. Old, classical pulsars: sensitivity to initial rotation rate González, R., & Fernández, in preparation

38. 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

39. Previous constraints on dG/dt

40. 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

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

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

43. Constraint from PSR J0437-4715:...if only modified Urca processes are allowed, and the star has reached its stationary state. Required time: Compare to age estimates: (Hansen & Phinney 1998)

44. Now :

45. Main uncertainties Atmospheric model: –Deviations from blackbody H atmosphere underpredicts Rayleigh-Jeans tail Neutrino emission mechanism/rate: –Slow (mod. Urca) vs. fast (direct Urca, others) –Cooper pairing (superfluidity): R. 1997; Villain & Haensel 2005; work in progress Not important (because stationary state): Heat capacity: steady state Heat transport through crust

46. Other heating mechanisms Accretion of interstellar gas: Only for slowly moving, slowly rotating and/or unmagnetized stars 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 Comparison of heating mechanisms: González, Reisenegger, & Fernández 2007 (in preparation)