2. The Cooling of Neutron Stars Dany Page Instituto de Astronomía, UNAM, Mexico KIAS - APCTP International Symposium in Astro-Hadron Physic Seoul, Korea, 10 - 14 November 2003

3. Neutrino Emission Scenarios Prologue... The previously denominated “Standard Cooling Model” Nucleon pairing introduces another neutrino process due to the FORMATION and BREAKING of COOPER PAIRS Flowers, Ruderman & Sutherland, Ap. J. 205 (1976), 541 Voskresenskii & Senatorov, Zh. Eksp. Teor. Fiz. 90 (1986), 1505 [JETP 63 (1986), 885] Voskresenskii & Senatorov, Yad. Fiz. 45 (1987), 657 [Sov. J. Nucl. Phys. 45 (1987), 411]

4. Minimal Cooling of Neutron Stars Dany Page Instituto de Astronomía, UNAM Ongoing collaboration with: J.H. Lattimer (SUNY Stony Brook) M. Prakash (SUNY Stony Brook) A. Steiner (UM, Mineapolis) Revised version of the “Standard Model” PART I

5. Motivation: Many new observations of cooling neutron stars with CHANDRA and XMM-NEWTON. Some have low estimates of T e Do we have any strong evidence for the presence of some “exotic” component in the core of some of these neutron stars ?

7. ATMOSPHERE : a few cm thick. Determines the spectrum: distribution of observable flux as a function of photon energy  Measurement of “surface” temperature ENVELOPE : a few tens of meter thick. Blanket which controls the outgoing heat flux  Luminosity CRUST : only important for the early cooling, little effect later on. OUTER CORE : n, p, e,  essential for neutrino emission, and thermal energy content INNER CORE : mystery. Assumed not to exist for now.

8. The Supranuclear Equation of State (EOS) for the Minimal Model

9. APR: Akmal & Pandharipande, Phys. Rev. C56 (1997), 2261 Akmal, Pandharipande & Ravenhall, Phys. Rev. C58 (1998), 1804 [AV18 potential + UIX 3body interaction +  v b boost] WFF3: Wiringa, Fiks & Fabrocini, Phys. Rev. C38 (1988), 1010 [UV14 potential + TNI 3body interaction] BPAL21 & BPAL31: Bombaci, Prakash, Ainsworth & Lattimer, Phys. Rep. 280, 1 (1997) [Parametric EOS which reproduces saturation properties, with S ~ n 1/2 ] Selection criteria for the supranuclear EOS: The only present baryons are neutrons and protons. (No meson condensate, no hyperons, no quark matter, no...) The proton fraction is sufficiently low that DURCA is not allowed. Point 2 eliminates most Effective Field Theoretical (EFT) models and relativistic Dirac-Brückner-Hartree-Fock (DBHF) models

10. PRESSURE vs. DENSITY 0 1 2 3 4 5 6 n B /n 0 n 0 = saturation density

11. Neutron Star MASS vs. RADIUS At 1.4 M o : R ~ 11 – 12 km At M Max : R ~ 9.5 – 10.5 km

12. NUCLEON EFFECTIVE MASS

13. Conclusions: Within the Minimal Model the EOS is pretty well defined. 1.4 M o neutron stars have radii ~ 11 - 12 km M Max neutron stars have radii ~ 9.5 – 10.5 km

14. The Envelope: (outer boundary condition) Sensitivity Strip Magnetic field Chemical composition

15. Temperature profile in the envelope: the “sensivity strip” Gudmundsson, Pethick & Epstein, Ap. J. 259 (1982), L19 and Ap. J. 272 (1983) 286

16. “T e – T b relationship” for dipolar and dipolar+quadrupolar fields Page & Sarmiento, 1996

17. M env = 0 Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

18. M env = 10 -17 M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

19. M env = 10 -15 M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

20. M env = 10 -13 M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

21. M env = 10 -11 M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

22. M env = 10 -9 M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

23. M env = 10 -7 M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

24. Neutrino Cooling era: L >> L  Photon Cooling era: L  << L  Basic Cooling: neutrino vs photon cooling eras

25. Effect of envelope chemical compositions Light elements envelope Iron-like envelope

26. Neutron and Proton Pairing

27. Predictions for the NEUTRON 1 S 0 gap WAP: Wambach, Ainsworth & Pines, Nulc. Phys. A555 (1993), 128 CCDK: Chen, Clark, Davé & Khodel, Nucl. Phys. A555 (1993), 59 SCLBL: Schulze, Cugnon, Lejeune, Baldo & Lombardo, Phys. Lett. B375 (1996), 1 SFB: Schwenk, Friman & Brown, Nucl. Phys. A717 (2003), 191  Crust-core transition Important feature: Medium polarization effects reduce T c by a factor three

28. Predictions for the PROTON 1 S 0 gap T: Takatsuka, Prog. Thero. Phys. 50 (1970), 905 CCY: Chao, Clark & Yang, Nucl. Phys. A179 (1972), 320 AO: Amundsen & Osgaard, Nucl. Phys. A437 (1985), 487 BCLL: Baldo, Cugnon, Lejeune & Lombardo, Nucl. Phys. A536 (1992), 349 CCDK: Chen, Clark, Davé & Khodel, Nucl. Phys. A555 (1993), 59 EEHO: Elgaroy, Engvik, Horth-Jensen & Osnes, Nucl. Phys. A604 (1996), 466 Important features: All vanish at p F >1.3 fm -1 and most at p F > 1 fm -1 Expected maximum T c ~ 1 - 2 x 10 9 K Medium polarization effects seem to reduce T c by a factor three

29. Predictions for the NEUTRON 3 P 2 gap 0: Hoffberg, Glassgold, Richardson & Ruderman, Phys. Rev. Lett. 24 (1970), 775 1: Amundsen & Osgaard, Nucl. Phys. A442 (1985), 4163 2: Takatsuka, Prog. Theor. Phys. 48 (1972), 1517 a, b, c: Baldo, Elgaroy, Engvik, Horth-Jensen & Schulze, Phys. Rev. C58 (1998), 1921 Important feature: WE DO NOT REALLY KNOW WHAT IT IS Medium polarization effects were expected to increase the 3 P 2 gap while they probably strongly suppress it.

30. Specific Heat and its Suppression by Pairing

31. Distribution of C v in the core among constituents At T=10 9 K

32. Pairing and neutrino emission: Supression Cooper pair formation and destruction

33. Suppression of MURCA et al. by pairing

34. Neutrino emission through the formation and breaking of Cooper pairs Flowers, Ruderman & Sutherland, Ap. J. 205 (1976), 541 Voskresenskii & Senatorov, Zh. Eksp. Teor. Fiz. 90 (1986), 1505 [JETP 63 (1986), 885] Voskresenskii & Senatorov, Yad. Fiz. 45 (1987), 657 [Sov. J. Nucl. Phys. 45 (1987), 411]

35. Cooper pair neutrino luminosities for p 1 S 0 and n 3 P 2 gaps (APR 1.4 M o )

36. Cooper Pair Neutrino Luminosities vs MURCA and Photons in complete realistic evolutionary calculations (APR 1.4 M o ) Neutron 3 P 2 gap “a”Neutron 3 P 2 gap “b”Neutron 3 P 2 gap “c” Proton 1 S 0 gap from Amundsen & Ostgaard

37. Variations on a theme: Varying the star´s mass Varying the EOS Cranking up the MURCA rate

38. Varying the star´s mass EOS: APR

39. Varying the EOS

40. Cranking up the MURCA rate (à la Friman & Maxwell)

41. Putting things together: Minimal Model (and all its uncertainties) vs. DATA (and all their uncertainties)

43. Everything together: All possible neutron and proton gaps Light element envelopes Heavy element envelopes

46. All possible neutron and proton gaps

47. Predictions for the NEUTRON 3 P 2 gap

48. Heavy elements envelopes Neutron 3 P 2 gap = 0 All possible n & p 1 S 0 gaps

49. Heavy elements envelopes Neutron 3 P 2 gap = "a" (T c ~10 9 K) All possible n & p 1 S 0 gaps

50. Heavy elements envelopes Neutron 3 P 2 gap = "b" (T c ~3x10 9 K) All possible n & p 1 S 0 gaps

51. Heavy elements envelopes Neutron 3 P 2 gap = "c" (T c ~10 10 K) All possible n & p 1 S 0 gaps

52. Heavy elements envelopes All possible n & p gaps

53. Light element envelopes All possible neutron and proton gaps

54. Light elements envelopes Neutron 3 P 2 gap = 0 All possible n & p 1 S 0 gaps

55. Light elements envelopes Neutron 3 P 2 gap = "a" (T c ~10 9 K) All possible n & p 1 S 0 gaps

56. Light elements envelopes Neutron 3 P 2 gap = "b" (T c ~3x10 9 K) All possible n & p 1 S 0 gaps

57. Light elements envelopes Neutron 3 P 2 gap = "c" (T c ~10 10 K) All possible n & p 1 S 0 gaps

58. Light elements envelopes All possible n & p gaps

59. Light element envelopes Iron envelopes Summary: Temperature vs Time

60. Summary: Luminosity vs Time

61. CONCLUSIONS about the THEORY EOS quite well determined The mass of the star has little impact The dominant neutrino emission process is from the formation and breaking of Cooper pairs from the neutron 3P2 gap (unless this gap is very small) Possibility of the presence of light elements in the envelope allows to accomodate a range of T e at a given age

62. CONCLUSIONS about COMPARISON with DATA Neutron 3P2 pairing with T c ~ 10 9 K and various envelope composition may be marginally acceptable.

63. CONCLUSIONS about COMPARISON with DATA Neutron 3P2 pairing with T c > 3x10 9 K and various envelope composition seems to be marginally inacceptable.

64. CONCLUSIONS about COMPARISON with DATA Neutron 3P2 pairing with T c ~ 0 is inacceptable and would requiere a more elaborate model but a vanishing neutron 3 P 2 gap is a serious problem

65. Fast Cooling of Neutron Stars PART II

66. ATMOSPHERE : a few cm thick. Determines the spectrum: distribution of observable flux as a function of photon energy  Measurement of “surface” temperature ENVELOPE : a few tens of meter thick. Blanket which controls the outgoing heat flux  Luminosity CRUST : only important for the early cooling, little effect later on. OUTER CORE : n, p, e,  essential for neutrino emission, and thermal energy content INNER CORE : mystery. ==> Strong neutrino emission

67. Neutrino Emission Scenarios

68. Fast Cooling with Direct Urca Process “The Cooling of Neutron Stars by the Direct Urca Process”, Page & Applegate, ApJ 394, L17 (1992) Critical mass for Durca: 1.35 M o Notice: the 1.4 M o star has a "Durca pit" of 0.04 M o ! <- Arbitrary, we DO NOT KNOW what it really is

69. Fast Cooling with Direct Urca Process “The Cooling of Neutron Stars by the direct Urca Process”, Page & Applegate, ApJ 394, L17 (1992) With pairing (e.g., n 3 P 2 ) the cooling can be temporarily stopped at practically any temperature, depending on the value of T c in the "Durca pit"

70. Fast Cooling with a Kaon Condensate “Strangeness Condensation, Nucleon Superfluidity, and Cooling of Neutron Stars”, Page & Baron, ApJ 354 L17 (1990)

71. Fast Neutrino Emission Scenarios Q         erg s -1 cm -3 [K - condensate]       erg s -1 cm -3  -  condensate        erg s -1 cm -3 [Direct URCA] From: D. Page, “Thermal Evolution of Isolated Neutron Stars”, in The Many Faces of Neutron Stars [NATO ASI, Lipari, 1996]

72. “Prospects of Detecting Baryon and Quark Superfluidity from Cooling Neutron Stars”, Page, Prakash, Lattimer & Steiner, PRL 85, 2048 (2000) A "Maximal Model" Direct Urcas with Nucleons, Hyperons and Quarks

73. J 44 = differential angular momentum in the frictionally coupled inner crust neutron superfluid, in units of 10 44 g cm 2 rad s -1 Fast Cooling with a Kaon Condensate with frictional heating and light element envelopes “Fast Cooling of Neutron Stars: Superfluidity versus Heating and Accreted Envelope”, Page, ApJ 479, L43 (1997)