Thermal Behavior of Neutron Stars

Transcription

1 Thermal Behavior of Neutron Stars Dany Page Instituto de Astronomía Universidad Nacional Autónoma de México 1

2 Thermal Behavior of Neutron Stars Overview of neutron star structure and a simple analytical cooling model The effect of nucleon pairing Uncertainties from structure of the envelope Minimal Cooling Examples of fast cooling scenarios Conclusion and prospects 2

3 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., 2006ARNPS P 3

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 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). neutron Of superfluid upmost importance for 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., 2006ARNPS P 4

5 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... 5

6 Surface photon emission on a napkin Lγ: erg s -1 Te: effective temperature, is defined by this relation (in analogy to blackbody emission) Relationship between Te and T=Tint (interior T): provided by an envelope model. Simple ( rule of thumb ) formula: 6

7 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 7

8 Neutrino emission on a napkin 8

9 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,

10 A sample of neutrino emission processes Modified URCA vs. Direct URCA: 3 vs 5 fermions phase space: 10

11 A simple analytical solution Neutrino Cooling Era: Lν >> Lγ Photon Cooling Era: Lγ >> Lν 11

12 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: 12

13 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) 13

14 Thermal Behavior of Neutron Stars Overview of neutron star structure and a simple analytical cooling model The effect of nucleon pairing Uncertainties from structure of the envelope Minimal Cooling Examples of fast cooling scenarios Conclusion and prospects 14

15 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,

16 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 16

17 Pairing Tc models Neutron 1 S0 Proton 1 S0 Neutron 3 P2 Size and extent of pairing gaps is highly uncertain 17

18 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 18

19 Thermal Behavior of Neutron Stars Overview of neutron star structure and a simple analytical cooling model The effect of nucleon pairing Uncertainties from structure of the envelope Minimal Cooling Examples of fast cooling scenarios Conclusion and prospects 19

20 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 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., 2006ARNPS P 20

21 Envelope models Ingredients: Thin plane parallel layer with m=m, r=r L=4πR 2 σte 4 uniform in the envelope Los Alamos opacity tables and equation of state for pure iron RESULT: Tb - Te relationship. Tb = T at ρb = g cm -3 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 21

22 Envelope models Ingredients: Thin plane parallel layer with m=m, r=r L=4πR 2 σte 4 uniform in the envelope Los Alamos opacity tables and equation of state for pure iron RESULT: Tb - Te relationship. Tb = T at ρb = g cm -3 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 22

23 Tb - Te relationship for heavy elements Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C 23

24 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 24

25 Light element envelopes ΔMlight = 0 ΔMlight = mass of light in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C 25

26 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 in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C 26

27 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 in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C 27

28 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 in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C 28

29 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 in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C 29

30 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 in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C 30

31 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 in the upper envelope Cooling Neutron Stars with Accreted Envelopes Chabrier, Gilles; Potekhin, Alexander Y.; Yakovlev, Dmitry G., 1997ApJ...477L..99C 31

32 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 32

33 Heat transport with magnetic fields F = κ T τ = electron relaxation time κ = ω B = eb m ec κ κ 0 κ κ κ = electron cyclotron frequency κ = κ = κ = κ 0 κ (ω B τ) 2 κ 0 ω B τ 1 + (ω B τ) 2 Radial field Tangential field 33

34 Surface temperature distributions With the Greenstein-Hartke interpolation formula one can take any field geometry at the surface (envelope) and calculate the surface temperature distribution: 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) 34

35 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) 35

36 Thermal Behavior of Neutron Stars Overview of neutron star structure and a simple analytical cooling model The effect of nucleon pairing Uncertainties from structure of the envelope Minimal Cooling Examples of fast cooling scenarios Conclusion and prospects 36

37 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? 37

38 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. 38

39 Neutrino emission from the breaking (and formation) of Cooper pair: 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,

40 Vector channel PBF suppression: Need to conserve vector current 40

41 Basic effects of pairing on the cooling With pairing but no PBF Without pairing 41

42 Basic effects of pairing on the cooling With pairing but no PBF Without pairing With pairing (and PBF) 42

43 Core: homogeneous matter Swiss cheese Lasagna Spaghetti B Crust: nuclei + neutron superfluid 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., 2006ARNPS P 43

44 Dominant neutrino processes in the crust Plasmon decay process Bremsstrahlung processes: Pair annihilation process: Photo-neutrino process: 44

45 Early cooling of the crust (without pairing) All neutrino processes 45

46 Early cooling of the crust (without pairing) No plasma neutrinos All neutrino processes 46

47 Early cooling of the crust (without pairing) No plasma neutrinos Only plasma neutrinos All neutrino processes 47

48 Early cooling of the crust (without pairing) No plasma neutrinos Only plasma neutrinos All neutrino processes Plasma + bremsstrahlung: e-e brem. e-ion brem. n-n brem. 48

49 Effects of neutron 1 S0 pairing (crust) No pairing (as previous case) 49

50 Effects of neutron 1 S0 pairing (crust) Only suppression of neutron Cv : shortens the thermal time-scale 50

51 Effects of neutron 1 S0 pairing (crust) Suppression of Cv and n-n brem. Only suppression of neutron Cv : shortens the thermal time-scale 51

52 Effects of neutron 1 S0 pairing (crust)... adding the PBF neutrinos without vector channel suppression... 52

53 Effects of neutron 1 S0 pairing (crust)... and with the vector channel suppression... adding the PBF neutrinos without vector channel suppression... 53

54 Effect of the size of the neutron 1 S0 gap T Crust Core GC (?) CCDK WAP SFB 54

55 Effect of the size of the neutron 1 S0 gap GC (?) T SFP WAP CCDK Without the vector channel suppression With the vector channel suppression T GC (?) SFP WAP CCDK 55

56 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 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., 2006ARNPS P 56

57 Pairing Tc models Neutron 1 S0 Proton 1 S0 Neutron 3 P2 Size and extent of pairing gaps is highly uncertain 57

58 PBF vs MURCA and Photons Neutron 3 P 2 gap a Neutron 3 P 2 gap b Neutron 3 P 2 gap c Proton 1 S 0 from Amundsen & Ostgaard 58

59 Effect of PBF without vector channel suppression Light element envelopes Heavy element envelopes Neutron 3 P2 gap a and the whole family of of 1 S0 gaps (n & p) Without vector channel suppression 59

60 Effect of PBF with vector channel suppression Light element envelopes Heavy element envelopes Neutron 3 P2 gap a and the whole family of of 1 S0 gaps (n & p) With vector channel suppression 60

61 Effect of vector channel suppression Light element envelopes Heavy element envelopes Neutron 3 P2 gap a and the whole family of of 1 S0 gaps (n & p) 61

62 Observational data 62

63 Minimal Cooling versus data 1. RX J (in SNR Puppis A) 2. 1E (in SNR PKS ) 3. PSR RX J (in SNR CTB 1) 5. PSR PSR (in SNR ``Vela'') 7. PSR PSR PSR (``Geminga'') 10. RX J RX J PSR (in Crab) A. CXO J (in SNR Cas A) B. PSR J (in SNR 3C58) C. PSR J (in SNR G ) D. RX J (in SNR CTA 1) Heavy elements envelopes Light elements envelopes A 0 B C a b c d D a.? (in SNR G ) b.? (in SNR G ) c.? (in SNR G ) d.? (in SNR G ) 63

64 Neutron star initial mass function Agreement of most observed isolated cooling neutron star with predictions of the minimal cooling paradigm may be due to the range of initial mass 64

65 Thermal Behavior of Neutron Stars Overview of neutron star structure and a simple analytical cooling model The effect of nucleon pairing Uncertainties from structure of the envelope Minimal Cooling Examples of fast cooling scenarios Conclusion and prospects 65

66 Core: homogeneous matter Swiss cheese Lasagna Spaghetti B Crust: nuclei + neutron superfluid 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? 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., 2006ARNPS P 66

67 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 67

68 A Maximal cooling model (?) Comparison of two models with n, p & hyperons (DUURCA with Λ is controlled by its 1 S0 gap) and n, p, hyperons + quarks (Quark DURCAs are strongly suppress by a very large gap) Because of the strong suppression of neutrino emission by large gaps, there is little difference between the two models. Prospects of Detecting Baryon and Quark Superfluidity from Cooling Neutron Stars, D Page, M Prakash, JM Lattimer & AW Steiner, 2000PhRvL P 68

69 Thermal Behavior of Neutron Stars Overview of neutron star structure and a simple analytical cooling model The effect of nucleon pairing Uncertainties from structure of the envelope Minimal Cooling Examples of fast cooling scenarios Conclusion and prospects 69

70 Conclusions and... Many possibilities for fast neutrino emission. Neutrino emission can be strongly suppressed by pairing. Minimal Cooling: most observed isolated cooling neutron star are OK. A few serious candidates for neutrino cooling beyond minimal. 70

71 ... prospects HELP! From nuclear physicists: Reliable pairing gaps (for nucleons, hyperons, quarks:!?!) Medium effects on the modified URCA process From astrophysicists: Better atmosphere models with strong magnetic fields Better models of Tsurf distribution with magnetic fields. From astronomers: More reliable estimates of ages X-ray polarimetry to determine the surface magnetic field geometry (?) 71

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