Neutron Star Cooling. Dany Page. Instituto de Astronomía Universidad Nacional Autónoma de México

Transcription

1 Neutron Star Cooling Dany Page Instituto de Astronomía Universidad Nacional Autónoma de México 1

2 Core: homogeneous matter Swiss cheese Lasagna Spaghetti B Crust: nuclei + neutron superfluid Atmosphere Envelope Crust Outer core Inner core A Neutron superfluid Neutron superfluid + proton superconductor Neutron vortex Neutron vortex Nuclei in a lattice Magnetic flux tube C Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints, Page D. & Reddy S., 2006, Annu. Rev. Nucl. Part. Sci. 56, 327 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

3 Core: homogeneous matter Swiss cheese Lasagna Spaghetti B Atmosphere (10 cm): Determines Crust: the shape of the thermal nuclei + radiation (the spectrum). Of neutron upmost importance for superfluid interpretation of X-ray (and optical) observation. However it as NO effect on the thermal evolution of the star. Atmosphere Envelope Crust Outer core Inner core A Neutron superfluid Neutron superfluid + proton superconductor Neutron vortex Neutron vortex Nuclei in a lattice Magnetic flux tube C Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints, Page D. & Reddy S., 2006, Annu. Rev. Nucl. Part. Sci. 56, 327 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

4 Envelope (100 m): Contains a huge temperature gradient: it determines the relationship between Tint and Te. Extremely important for the cooling, strongly affected by magnetic fields and the presence of polluting light elements. Core: homogeneous matter Swiss cheese Lasagna Spaghetti B Atmosphere (10 cm): Determines Crust: the shape of the thermal nuclei + radiation (the spectrum). Of neutron upmost importance for superfluid interpretation of X-ray (and optical) observation. However it as NO effect on the thermal evolution of the star. Atmosphere Envelope Crust Outer core Inner core A Neutron superfluid Neutron superfluid + proton superconductor Neutron vortex Neutron vortex Nuclei in a lattice Magnetic flux tube C Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints, Page D. & Reddy S., 2006, Annu. Rev. Nucl. Part. Sci. 56, 327 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

5 Envelope (100 m): Contains a huge temperature gradient: it determines the relationship between Tint and Te. Extremely important for the cooling, strongly affected by magnetic fields and the presence of polluting light elements. Core: homogeneous matter Swiss cheese Lasagna Spaghetti B Atmosphere (10 cm): Determines Crust: the shape of the thermal nuclei + radiation (the spectrum). Of neutron upmost importance for superfluid interpretation of X-ray (and optical) observation. However it as NO effect on the thermal evolution of the star. Atmosphere Envelope Crust Outer core Inner core Crust (1 km): Little effect on the long term cooling. BUT: may contain A heating sources (magnetic/ rotational, pycnonuclear under accretion). Its thermal time is important for very young star and for quasi-persistent accretion Neutron superfluid Neutron superfluid + proton superconductor Neutron vortex Neutron vortex Nuclei in a lattice Magnetic flux tube C Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints, Page D. & Reddy S., 2006, Annu. Rev. Nucl. Part. Sci. 56, 327 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

6 Envelope (100 m): Contains a huge temperature gradient: it determines the relationship between Tint and Te. Extremely important for the cooling, strongly affected by magnetic fields and the presence of polluting light elements. Core: homogeneous matter Swiss cheese Lasagna Spaghetti B Atmosphere (10 cm): Determines Crust: the shape of the thermal nuclei + radiation (the spectrum). Of neutron upmost importance for superfluid interpretation of X-ray (and optical) observation. However it as NO effect on the thermal evolution of the star. Atmosphere Envelope Crust Outer core Inner core Crust (1 km): Little effect on the long term cooling. BUT: may contain A heating sources (magnetic/ rotational, pycnonuclear under accretion). Its thermal time is important for very young star and for quasi-persistent accretion Neutron superfluid Neutron superfluid + proton superconductor Neutron vortex Neutron vortex Nuclei in a lattice Magnetic flux tube Outer Core (10-x km): Nuclear and supranuclear densities, C containing n, p, e & µ. Provides about 90% of cv and εν unless an inner core is present. Its physics is basically under control except pairing Tc which is essentially unknown. Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints, Page D. & Reddy S., 2006, Annu. Rev. Nucl. Part. Sci. 56, 327 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

7 Envelope (100 m): Contains a huge temperature gradient: it determines the relationship between Tint and Te. Extremely important for the cooling, strongly affected by magnetic fields and the presence of polluting light elements. Core: homogeneous matter Crust (1 km): Little effect on the long term cooling. BUT: may contain A heating sources (magnetic/ rotational, pycnonuclear under accretion). Its thermal time is important for very young star and for quasi-persistent accretion Swiss cheese Lasagna Spaghetti Inner Core (x km?): The hypothetical region. Possibly only present in massive NSs. May contain Λ, Σ -, Σ 0, π or K condensates, or/and deconfined quark matter. Its εν dominates the outer core by many orders of magnitude. Tc? B Neutron superfluid Neutron superfluid + proton superconductor Neutron vortex Neutron vortex Nuclei in a lattice Magnetic flux tube Atmosphere (10 cm): Determines Crust: the shape of the thermal nuclei + radiation (the spectrum). Of neutron upmost importance for superfluid interpretation of X-ray (and optical) observation. However it as NO effect on the thermal evolution of the star. Atmosphere Envelope Crust Outer core Inner core Outer Core (10-x km): Nuclear and supranuclear densities, C containing n, p, e & µ. Provides about 90% of cv and εν unless an inner core is present. Its physics is basically under control except pairing Tc which is essentially unknown. Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints, Page D. & Reddy S., 2006, Annu. Rev. Nucl. Part. Sci. 56, 327 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

8 Neutron star cooling on a napkin Assume the star s interior is isothermal and neglect GR effects. Thermal Energy, Eth,balance: 3 essential ingredients are needed: Cv = total stellar specific heat Lγ = total surface photon luminosity L ν = total stellar neutrino luminosity H = heating, from B field decay, friction, etc... Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

9 Observational Data 4

10 Observational data PSR J (in Puppis A) PSR 1E PSR J PSR B PSR B (in Vela) PSR B PSR B RX J RX J PSR B ("Geminga") PSR B PSR B CXO J (in Cas A) (? in G ) (? in G ) (? in G ) PSR B (in Crab) PSR J RX J PSR J (in 3C58) PSR J (in CTA 1) (? in G ) (? in G ) (? in G ) Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

11 Specific Heat 6

12 Neutron star cooling on a napkin Assume the star s interior is isothermal and neglect GR effects. Thermal Energy, Eth,balance: 3 essential ingredients are needed: Cv = total stellar specific heat Lγ = total surface photon luminosity L ν = total stellar neutrino luminosity H = heating, from B field decay, friction, etc... Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

13 Specific heat on a napkin Sum over all degenerate fermions: (lowest value corresponds to the case where extensive pairing of baryons in the core suppresses their cv and only the leptons, e & µ, contribute) Distribution of cv in the core of a 1.4 MSun neutron star build with the APR EOS (Akmal, Pandharipande, & Ravenhall, 1998), at T = 10 9 K Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

14 Neutrinos 9

15 The direct Urca process Basic mechanism: β and inverse β decays: Direct URCA process in neutron stars, JM Lattimer, CJ Pethick, M Prakash & P Haensel, 1991 PhRvL 66, 2701 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

16 The direct Urca process Basic mechanism: β and inverse β decays: Energy conservation: EFn = EFp + EFe e - n p Direct URCA process in neutron stars, JM Lattimer, CJ Pethick, M Prakash & P Haensel, 1991 PhRvL 66, 2701 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

17 The direct Urca process Basic mechanism: β and inverse β decays: Energy conservation: Momentum conservation: EFn = EFp + EFe e - Triangle rule : pfn < pfp + pfe n p Direct URCA process in neutron stars, JM Lattimer, CJ Pethick, M Prakash & P Haensel, 1991 PhRvL 66, 2701 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

18 The modified URCA process If the direct Urca process: is forbidden because of momentum conservation, add a spectator neutron: Modified Urca process: Momentum conservation is automatic, but the price to pay is: 3 vs 5 fermions phase space: Direct URCA process in neutron stars, JM Lattimer, CJ Pethick, M Prakash & P Haensel, 1991 PhRvL 66, 2701 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

19 Neutrino emission on a napkin (I) The Murca-Bremsstrahlung family and Durca Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

20 Hyperons in neutron stars (I) Hyperons, as Λ and Σ - can be produced through reactions as, e.g. Energy conservation requires: Momentum conservation: very easily satisfied for Λ and not very difficult to satisfy for Σ - Hyperons will result in DUrca processes if they can be present Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

21 Charged mesons (π - & K - ) in neutron stars Hyperons, as π - and K - can be produced through reactions as, e.g. Energy conservation requires: Momentum conservation: trivially satisfied because mesons condense (they are bosons) and the condensate can absorb any extra needed momentum Charged mesons will result in DUrca processes if they can be present Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

22 Neutrino emission on a napkin (III) Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

23 Neutrino emission on a napkin (III) Anything beyond just neutrons and protons (and only a small amount of them) results in enhanced neutrino emission Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

24 Dominant neutrino processes in the crust Plasmon decay process Bremsstrahlung processes: Pair annihilation process: Photo-neutrino process: Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

25 Simple Models 17

26 A simple analytical solution Neutrino Cooling Era: Lν >> Lγ Photon Cooling Era: Lγ >> Lν Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

27 Neutrino cooling time scales Slow neutrino cooling: (lowest value corresponds to the case where extensive pairing in the core suppresses its neutrino emission and only the crust e-ion bremsstrahlung process is active) Fast neutrino cooling: Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

28 MUrca vs DUrca 20

29 Direct vs modified Urca cooling Models based on the PAL EOS: SLOW adjusted (by hand) so that DURCA becomes allowed (triangle rule!) at M > 1.35 MSun. FAST The Cooling of Neutron Stars by the Direct Urca Process, Page & Applegate, ApJ 394, L17 (1992) Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

30 Direct vs modified Urca cooling Models based on the PAL EOS: SLOW adjusted (by hand) so that DURCA becomes allowed (triangle rule!) at M > 1.35 MSun. FAST This value is arbitrary: we DO NOT know the value of this critical mass, and hopefully observations will, some day, tell us what it is! The Cooling of Neutron Stars by the Direct Urca Process, Page & Applegate, ApJ 394, L17 (1992) Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

31 Standard cooling of a 1.3 Mʘ neutron star 22

32 Standard cooling of a 1.3 Mʘ neutron star Atmosphere Envelope Core Crust 23

33 Standard cooling of a 1.3 Mʘ neutron star Relaxation from (arbitrary) initial condition Atmosphere Envelope Crust Core 24

34 Standard cooling of a 1.3 Mʘ neutron star Relaxation from (arbitrary) initial condition Atmosphere Envelope Crust Core Early plateau: controlled by plasma neutrinos from the outer crust (envelope) 24

35 Standard cooling of a 1.3 Mʘ neutron star Relaxation from (arbitrary) initial condition Isothermalization: crustal heat flows into the core and is lost in neutrinos Atmosphere Envelope Crust Core Early plateau: controlled by plasma neutrinos from the outer crust (envelope) 24

36 Standard cooling of a 1.3 Mʘ neutron star Relaxation from (arbitrary) initial condition Isothermalization: crustal heat flows into the core and is lost in neutrinos Atmosphere Envelope Crust Core Neutrino cooling era Early plateau: controlled by plasma neutrinos from the outer crust (envelope) 24

37 Standard cooling of a 1.3 Mʘ neutron star Relaxation from (arbitrary) initial condition Isothermalization: crustal heat flows into the core and is lost in neutrinos Atmosphere Envelope Crust Core Neutrino cooling era Photon cooling era Early plateau: controlled by plasma neutrinos from the outer crust (envelope) 24

38 Standard cooling of a 1.3 Mʘ neutron star See file Movie_1a.gif 25

39 Direct vs modified Urca cooling Models based on the PAL EOS: SLOW adjusted (by hand) so that DURCA becomes allowed (triangle rule!) at M > 1.35 MSun. FAST This value is arbitrary: we DO NOT know the value of this critical mass, and hopefully observations will, some day, tell us what it is! The Cooling of Neutron Stars by the Direct Urca Process, Page & Applegate, ApJ 394, L17 (1992) Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

40 Enhanced cooling of a 1.5 Mʘ neutron star Atmosphere Envelope Core Crust 27

41 Enhanced cooling of a 1.5 Mʘ neutron star Outer core: MUrca Inner core: DUrca Atmosphere Envelope Core Crust 28

42 Enhanced cooling of a 1.5 Mʘ neutron star See file Movie_1b.gif 29

43 Pairing 30

44 Nucleon pairing Gap Possible Analogy between the Excitation Spectra of Nuclei and Those of the Superconducting Metallic State, Bohr, Mottelson, Pines, 1958 Phys. Rev. 110, 936 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

45 Suppression of cv and εν by pairing The presence of a pairing gap in the single particple excitation spectrum results in a Boltzmann-like exp(-δ/kbt) suppression of cv and εν: Control factor Rc Cv Control factor Rν εν Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

46 Pairing Tc models Neutron 1 S0 Proton 1 S0 Neutron 3 P2 Size and extent of pairing gaps is highly uncertain Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

47 Slow vs fast cooling with pairing Slow neutrino emission (modified URCA process) Standard cooling Slow cooling Fast cooling 24 n = Fast neutrino emission (almost anything else) SF N SF n = 24 Kaon condensate n = 25 Pion condensate n = 26 Direct Urca N Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

48 Slow vs fast cooling with pairing Slow neutrino emission (modified URCA process) Fast neutrino emission (almost anything else) Standard cooling Slow cooling Fast cooling A large enough Tc for pairing (superfluidity or superconductivity) can transform fast cooling into moderate cooling n = 24 Kaon condensate n = 25 Pion condensate n = 26 Direct Urca n = SF N SF N Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

49 Standard cooling of a 1.3 Mʘ neutron star with pairing See file Movie_2a.gif 36

50 Enhanced cooling of a 1.5 Mʘ neutron star with pairing Envelope Crust Outer Core Inner Core 37

51 Enhanced cooling of a 1.5 Mʘ neutron star moderated pairing See file Movie_2b.gif 38

52 Envelopes: Heavy vs light elements Magnetic fields 39

53 Envelope (100 m): Contains a huge temperature gradient: it determines the relationship between Tint and Te. Extremely important for the cooling, strongly affected by magnetic fields and the presence of polluting light elements. Core: homogeneous matter Swiss cheese Lasagna Spaghetti B Atmosphere (10 cm): Determines Crust: the shape of the thermal nuclei + radiation (the spectrum). Of neutron upmost importance for superfluid interpretation of X-ray (and optical) observation. However it as NO effect on the thermal evolution of the star. Atmosphere Envelope Crust Outer core Inner core A Neutron superfluid Neutron superfluid + proton superconductor Neutron vortex Neutron vortex Nuclei in a lattice Magnetic flux tube C Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints, Page D. & Reddy S., 2006, Annu. Rev. Nucl. Part. Sci. 56, 327 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

54 Envelope models Neutron star envelopes Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I., 1982ApJ...259L..19G Structure of neutron star envelopes Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I. 1983ApJ G Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

55 Tb - Te relationship for heavy elements Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

56 Tb - Te relationship for heavy elements Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

57 The sensitivity strip Structure of neutron star envelopes Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I. 1983ApJ G Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

58 The sensitivity strip Crystalized ions: high thermal conductivity Structure of neutron star envelopes Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I. 1983ApJ G Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

59 The sensitivity strip photons transport heat: very efficient Crystalized ions: high thermal conductivity Structure of neutron star envelopes Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I. 1983ApJ G Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

60 The sensitivity strip photons transport heat: very efficient What happens if the physics in the sensitivity layer is altered: light elements? magnetic fields? Crystalized ions: high thermal conductivity Structure of neutron star envelopes Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I. 1983ApJ G Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

61 Light element envelopes ΔMlight = 0 ΔMlight = mass of light elements in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

62 Thickness of light elements layer Light element envelopes ΔMlight = MSun Electron thermal conductivity, due to e-ion scattering in the liquid sensitivity layer: ΔMlight = mass of light elements in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

63 Thickness of light elements layer Light element envelopes ΔMlight = MSun Electron thermal conductivity, due to e-ion scattering in the liquid sensitivity layer: ΔMlight = mass of light elements in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

64 Thickness of light elements layer Light element envelopes ΔMlight = MSun Electron thermal conductivity, due to e-ion scattering in the liquid sensitivity layer: ΔMlight = mass of light elements in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

65 Thickness of light elements layer Light element envelopes ΔMlight = MSun Electron thermal conductivity, due to e-ion scattering in the liquid sensitivity layer: ΔMlight = mass of light elements in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

66 Thickness of light elements layer Light element envelopes ΔMlight = 10-9 MSun Electron thermal conductivity, due to e-ion scattering in the liquid sensitivity layer: ΔMlight = mass of light elements in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

67 Thickness of light elements layer Light element envelopes ΔMlight = 10-7 MSun Electron thermal conductivity, due to e-ion scattering in the liquid sensitivity layer: ΔMlight = mass of light elements in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

68 Light element envelopes 10-7 Msun is about the maximum possible amount of light elements: pycnonuclear reaction will fuse them into heavier elements at higher densities Thickness of light elements layer ΔMlight = 10-7 MSun Electron thermal conductivity, due to e-ion scattering in the liquid sensitivity layer: ΔMlight = mass of light elements in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

69 Effect of light element envelopes Heavy element envelope Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

70 Effect of light element envelopes Light element envelope Heavy element envelope Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

71 Effect of light element envelopes Light element envelope Heavy element envelope Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

72 Effect of light element envelopes Light element envelope Heavy element envelope Light element envelopes: - star looks warmer during neutrino cooling era, but - cools faster during photon cooling era Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

73 Magnetized envelopes: surface temperature distributions Purely dipolar field (oriented on the equatorial plane to make a prettier picture!) Dipolar + quadrupolar field Surface temperature of a magnetized neutron star and interpretation of the ROSAT data. I. Dipolar fields D Page, ApJ 442, 273 (1995) Surface temperature of a magnetized neutron star and interpretation of the ROSAT data. II. D Page & A Sarmiento, ApJ 473, 1067 (1996) Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

74 Magnetized Tb - Te relationships The star s effective temperature is then easily calculated: This directly generates a Tb - Te relationship for any surface magnetic field geometry Surface temperature of a magnetized neutron star and interpretation of the ROSAT data. II. D Page & A Sarmiento, ApJ 473, 1067 (1996) Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

75 Magnetized Tb - Te relationships The star s effective temperature is then easily calculated: This directly generates a Tb - Te relationship for any surface magnetic field geometry Surface temperature of a magnetized neutron star and interpretation of the ROSAT data. II. D Page & A Sarmiento, ApJ 473, 1067 (1996) Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

76 Comparison with Data 55

77 Direct Urca with pairing vs data EOS: PAL Mcr = 1.35 MSun Pairing gaps: Neutron 1 S0: SFB Neutron 3 P2: b Proton 1 S0: T73 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

78 Minimal Cooling 57

79 Minimal Cooling or, do we need fast cooling? Motivation: Many new observations of cooling neutron stars with CHANDRA and XMM-NEWTON Do we have any strong evidence for the presence of some exotic component in the core of some of these neutron stars? Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

80 Minimal Cooling or, do we need fast cooling? Minimal Cooling assumes: nothing special happens in the core, i.e., no direct URCA, no π - or K - condensate, no hyperons, no deconfined quark matter, no... (and no medium effects enhance the modified URCA rate beyond its standard value) Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

81 Minimal Cooling or, do we need fast cooling? Minimal Cooling assumes: nothing special happens in the core, i.e., no direct URCA, no π - or K - condensate, no hyperons, no deconfined quark matter, no... (and no medium effects enhance the modified URCA rate beyond its standard value) Minimal Cooling is not naive cooling: it takes into account uncertainties due to Large range of predicted values of Tc for n & p. Enhanced neutrino emission at T Tc from the Cooper pair formation mechanism. Chemical composition of upper layers (envelope), i.e., iron-peak elements or light (H, He, C, O,...) elements, the latter significantly increasing Te for a given Tb. Equation of state. Magnetic field. Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

82 Neutrino emission from the breaking (and formation) of Cooper pairs: PBF Neutrino pair emission from finite-temperature neutron superfluid and the cooling of neutron stars E Flowers, M Ruderman & P Sutherland, 1976ApJ F Voskresensky D., Senatorov A., 1986, Sov. Phys. JETP 63, 885 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

83 Basic effects of pairing on the cooling With pairing but no PBF Without pairing Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

84 Basic effects of pairing on the cooling With pairing but no PBF Without pairing With pairing (and PBF) Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

85 Pairing Tc models Neutron 1 S0 Proton 1 S0 Neutron 3 P2 Size and extent of pairing gaps is highly uncertain Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

86 Minimal cooling versus data Light element envelopes 3 Neutron P gap = Neutron P gap = "b" 2 Heavy element envelopes 3 Neutron P 2 gap = "a" 3 Neutron P gap = "c" 2 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

87 Minimal cooling versus data Light element envelopes 3 Neutron P gap = Neutron P gap = "b" 2 Heavy element envelopes 3 Neutron P gap = "a" With a small enough Tc for pairing 2 minimal cooling can explain (almost) 3 Neutron P gap = "c" all present data on cooling neutron stars 2 Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April

88 Conclusions 65

89 Conclusions Many possibilities for fast neutrino emission. Neutrino emission can be strongly suppressed by pairing. Fast cooling scenarios are compatible with if Tc for pairing is large enough. Minimal Cooling: most observed isolated cooling neutron stars are OK. A few serious candidates for neutrino cooling beyond minimal. Dany Page Neutron Star Cooling Arizona State University, Tempe 15 April