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					Thermal Behavior
       of
  Neutron Stars
              Dany Page

         Instituto de Astronomía
Universidad Nacional Autónoma de México


                                          1
                      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




Dany Page      Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009   2
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                                             La
                            Core:                                                                  Crust:
                                                                                                   nuclei
                     homogeneous                                                                     +
                          matter                                                                   neutron
                                                                                                   superfluid




                                                                                             Atmosphere
                                                                                             Envelope
                                                                                             Crust
                                                                                             Outer core
                                                                                             Inner core




                                                                                                         C
                        A
                                            Neutron superfluid Neutron superfluid
                                                                        +
                                                              proton superconductor
                                            Neutron vortex
                                                                     Neutron vortex
                                            Nuclei in a lattice Magnetic flux tube


                         “Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints”, Page D. & Reddy S., 2006ARNPS..56..327P

Dany Page   Thermal Behavior of Neutron Stars                    “Nuclear Matter at High Density”, Hirschegg, January 2009                              3
   Envelope (100 m):                                                                                 Atmosphere (10 cm):




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                                                  La
 Contains a huge temperatureCore:                                                                   Determines the shape of the
                                                                                                      Crust:
 gradient: it determines the
                         homogeneous                                                                thermal radiation (the spectrum).
                                                                                                      nuclei
                                                                                                        +
                                                                                                      neutron
                                Te.
 relationship between Tint andmatter                                                                    upmost
                                                                                                    Ofsuperfluid importance for
 Extremely important for the                                                                        interpretation of X-ray (and
 cooling, strongly affected by                                                                      optical) observation.
 magnetic fields and the presence                                                                    However it as NO effect on the
 of “polluting” light elements.                                                                     thermal evolution of the star.
                                             Inner Core (x km ?):          Atmosphere
                                                                           Envelope
                                          The hypothetical region.         Crust
                                          Possibly only present in massive Outer core
                                          NSs. May contain Λ, Σ-, Σ0, π or Inner core
                                          K condensates, or/and
                                          deconfined quark matter. Its εν
                                          dominates the outer core by
                                          many orders of magnitude. Tc ?
        Crust (1 km):                                                                                Outer Core (10-x km):
 Little effect on the long term                                                                     Nuclear and supranuclear
 cooling. BUT: may contain                                                                                C
                                                                                                    densities, containing n, p, e & µ.
                             A
 heating sources (magnetic/                      Neutron superfluid Neutron superfluid              Provides about 90% of cv and εν
 rotational, pycnonuclear under                                              +
                                                                   proton superconductor            unless an inner core is present.
                                                 Neutron vortex
 accretion). Its thermal time is                                          Neutron vortex            Its physics is basically under
 important for very young star                   Nuclei in a lattice Magnetic flux tube             control except pairing Tc which
 and for quasi-persistent accretion                                                                 is essentially unknown.
                              “Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints”, Page D. & Reddy S., 2006ARNPS..56..327P

Dany Page       Thermal Behavior of Neutron Stars                     “Nuclear Matter at High Density”, Hirschegg, January 2009                              4
                  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
                     • Lν = total stellar neutrino luminosity

                                                H = “heating”, from B field decay, friction, etc ...
Dany Page   Thermal Behavior of Neutron Stars      “Nuclear Matter at High Density”, Hirschegg, January 2009   5
               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:




Dany Page      Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009   6
                             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 = 109 K




Dany Page     Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009                   7
                    Neutrino emission on a napkin




Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009   8
                              The direct URCA process

                 Basic mechanism: β and inverse β decays:



    Energy conservation:                                      Momentum conservation:
            EFn = EFp + EFe                             “Triangle rule”:                                 pFn < pFp + pFe
                                    e-

            n
                                     p


                                           “Direct URCA process in neutron stars”, JM Lattimer, CJ Pethick, M Prakash & P Haensel, 1991 PhRvL 66, 2701

Dany Page       Thermal Behavior of Neutron Stars             “Nuclear Matter at High Density”, Hirschegg, January 2009                                  9
            A sample of neutrino emission processes




              Modified URCA vs. Direct URCA:




                  3 vs 5 fermions phase space:




Dany Page    Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 10
                           A simple analytical solution




    •   Neutrino Cooling Era: Lν >> Lγ




    •   Photon Cooling Era: Lγ >> Lν




Dany Page      Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 11
                          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      Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 12
                  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.



                                                                            This value is arbitrary:
                                                                            we DO NOT know the value of
                                                                            this critical mass, and hopefully
                                                                            observations will, some day, tell
                 FAST                                                       us what it is !




                                      “The Cooling of Neutron Stars by the Direct Urca Process”, Page & Applegate, ApJ 394, L17 (1992)
Dany Page   Thermal Behavior of Neutron Stars          “Nuclear Matter at High Density”, Hirschegg, January 2009 13
                      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




Dany Page      Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 14
                                                      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   Thermal Behavior of Neutron Stars                              “Nuclear Matter at High Density”, Hirschegg, January 2009 15
                    Suppression of cv and εν by pairing

            The presence of a pairing gap
                                                                                Cv




                                                         Control factor Rc
                in the single particple
            excitation spectrum results in
                   a Boltzmann-like

                    exp(-Δ/kBT)
              suppression of cv and εν:




                                                            Control factor Rν
                                                                                εν




Dany Page        Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 16
                                   Pairing Tc models

            Neutron 1S0                         Proton 1S0                       Neutron 3P2




                     Size and extent of pairing gaps is highly uncertain




Dany Page   Thermal Behavior of Neutron Stars     “Nuclear Matter at High Density”, Hirschegg, January 2009 17
                        Slow vs fast cooling with pairing

            Slow neutrino emission                           Standard cooling
                                                           “Slow cooling”
            (modified URCA process)                                           24
                                                            “Fast
                                                             Fast    n=
                                                             cooling          25
                                                            cooling”
                                                                              26
       Fast neutrino emission
       (almost anything else)                                                      SF

                                                                                   N
                                                                                   SF




      •     n = 24   Kaon condensate                                               N

      •     n = 25   Pion condensate
      •     n = 26   Direct Urca




Dany Page        Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 18
                      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




Dany Page      Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 19
   Envelope (100 m):




                                                           tti
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                                                        he
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                                                        g
                                                  ch iss




                                                    ag
                                                     sa
                                                    ee
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                                                  La
 Contains a huge temperatureCore:                                                                       Crust:
 gradient: it determines the
                         homogeneous
                                                                                                        nuclei
                                                                                                          +
                                                                                                        neutron
                                Te.
 relationship between Tint andmatter                                                                    superfluid
 Extremely important for the
 cooling, strongly affected by
 magnetic fields and the presence
 of “polluting” light elements.
                                                                                                  Atmosphere
                                                                                                  Envelope
                                                                                                  Crust
                                                                                                  Outer core
                                                                                                  Inner core




                                                                                                              C
                            A
                                                 Neutron superfluid Neutron superfluid
                                                                             +
                                                                   proton superconductor
                                                 Neutron vortex
                                                                          Neutron vortex
                                                 Nuclei in a lattice Magnetic flux tube


                              “Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints”, Page D. & Reddy S., 2006ARNPS..56..327P

Dany Page       Thermal Behavior of Neutron Stars                     “Nuclear Matter at High Density”, Hirschegg, January 2009 20
                                                                    Envelope models
  Ingredients:

  Thin plane parallel layer with

  m=M, r=R

  L=4πR2 σTe4 uniform in
              the envelope




   Los Alamos opacity tables
   and equation of state for pure
   iron


                                 RESULT: “Tb - Te” relationship. Tb = T at ρB = 1010 g cm-3
Neutron star envelopes                                                                  Structure of neutron star envelopes
Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I., 1982ApJ...259L..19G                 Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I. 1983ApJ...272..286G

Dany Page                   Thermal Behavior of Neutron Stars             “Nuclear Matter at High Density”, Hirschegg, January 2009 21
                                                                    Envelope models
  Ingredients:

  Thin plane parallel layer with

  m=M, r=R

  L=4πR2 σTe4 uniform in
              the envelope




   Los Alamos opacity tables
   and equation of state for pure
   iron


                                 RESULT: “Tb - Te” relationship. Tb = T at ρB = 1010 g cm-3
Neutron star envelopes                                                                  Structure of neutron star envelopes
Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I., 1982ApJ...259L..19G                 Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I. 1983ApJ...272..286G

Dany Page                   Thermal Behavior of Neutron Stars             “Nuclear Matter at High Density”, Hirschegg, January 2009 22
            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   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 23
                                  The sensitivity strip

                                                                What happens if the physics
                                                              in the sensitivity layer is altered:
                                                                       light elements ?
               photo
                      ns tra                                          magnetic fields ?
                             nspor
                     very e         t hea
                            fficien       t:
                                    t

                                                                                       hig Crys
                                                                                          h th tali
                                                                                              erm zed
                                                                                                 al c ion
                                                                                                     ond s:
                                                                                                        uct
                                                                                                            ivit
                                                                                                                y




                                                              Structure of neutron star envelopes
                                                              Gudmundsson, E. H.; Pethick, C. J.; Epstein, R. I. 1983ApJ...272..286G

Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 24
                           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

Dany Page   Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 25
                           Light element envelopes
                                                   Thickness
                                                               of light ele
                                                                               ments laye
                                                                                               r




                                                                                                     Electron thermal
                                                                                                   conductivity, due to
                                                                                                    e-ion scattering in
                                                                                                   the liquid sensitivity
                                                                                                           layer:
                                            ΔMlight = 10-17 MSun




            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

Dany Page   Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 26
                           Light element envelopes
                                                   Thickness
                                                               of light ele
                                                                               ments laye
                                                                                               r




                                                                                                     Electron thermal
                                                                                                   conductivity, due to
                                                                                                    e-ion scattering in
                                                                                                   the liquid sensitivity
                                                                                                           layer:
                                            ΔMlight = 10-15 MSun




            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

Dany Page   Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 27
                           Light element envelopes
                                                   Thickness
                                                               of light ele
                                                                               ments laye
                                                                                               r




                                                                                                     Electron thermal
                                                                                                   conductivity, due to
                                                                                                    e-ion scattering in
                                                                                                   the liquid sensitivity
                                                                                                           layer:
                                            ΔMlight = 10-13 MSun




            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

Dany Page   Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 28
                           Light element envelopes
                                                   Thickness
                                                               of light ele
                                                                               ments laye
                                                                                               r




                                                                                                     Electron thermal
                                                                                                   conductivity, due to
                                                                                                    e-ion scattering in
                                                                                                   the liquid sensitivity
                                                                                                           layer:
                                            ΔMlight = 10-11 MSun




            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

Dany Page   Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 29
                           Light element envelopes
                                                   Thickness
                                                               of light ele
                                                                               ments laye
                                                                                               r




                                                                                                     Electron thermal
                                                                                                   conductivity, due to
                                                                                                    e-ion scattering in
                                                                                                   the liquid sensitivity
                                                                                                           layer:
                                            ΔMlight = 10-9 MSun




            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

Dany Page   Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 30
                           Light element envelopes
                                                   Thickness
                                                               of light ele
                                                                               ments laye
                                                                                               r




                                                                                                     Electron thermal
                                                                                                   conductivity, due to
                                                                                                    e-ion scattering in
                                                                                                   the liquid sensitivity
                                                                                                           layer:
                                            ΔMlight = 10-7 MSun




            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

Dany Page   Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 31
                   Effect of light element envelopes



                               t
                            en
                        lem pe        e nt
                     t e elo        m
                  igh nv
                 L e             ele pe
                              vy elo
                            ea nv
                          H e




        Light element envelopes:
        - star looks warmer during
        neutrino cooling era, but
        - cools faster during photon
        cooling era

Dany Page    Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 32
                          Heat transport with magnetic fields
                                                                                   
                F = −κ ·          T                         κ⊥           κ∧    0                   κ = κ0
                                                      κ =  −κ∧          κ⊥    0                        κ0
                                                                                               κ⊥ =
                                                             0            0    κ                    1 + (ωB τ )2
                                                                                                      κ0 ω B τ
                                                             eB = electron cyclotron           κ∧ =
            τ = electron relaxation time              ωB =
                                                             m∗ c    frequency
                                                                                                    1 + (ωB τ )2
                                                              e




                                       Radial field                         Tangential field




Dany Page            Thermal Behavior of Neutron Stars           “Nuclear Matter at High Density”, Hirschegg, January 2009 33
                                    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.    Surface temperature of a magnetized neutron star and interpretation of the ROSAT data. II.
I. Dipolar fields                                                                          D Page & A Sarmiento, ApJ 473, 1067 (1996)
D Page, ApJ 442, 273 (1995)

Dany Page                  Thermal Behavior of Neutron Stars                             “Nuclear Matter at High Density”, Hirschegg, January 2009 34
                     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     Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 35
                      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




Dany Page      Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 36
            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    Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 37
            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     Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 38
            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...205..541F

                                  Voskresensky D., Senatorov A., 1986, Sov. Phys.–JETP 63, 885

Dany Page    Thermal Behavior of Neutron Stars                    “Nuclear Matter at High Density”, Hirschegg, January 2009 39
                 Vector channel PBF suppression:
                 Need to conserve vector current




Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 40
            Basic effects of pairing on the cooling


                                         With pairing but no PBF




                                    Without pairing




Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 41
            Basic effects of pairing on the cooling


                                         With pairing but no PBF




                                    Without pairing




                           With pairing (and PBF)




Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 42
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                                                 La
                              Core:                                                                    Crust:
                                                                                                       nuclei
                        homogeneous                                                                      +
                             matter                                                                    neutron
                                                                                                       superfluid




                                                                                                 Atmosphere
                                                                                                 Envelope
                                                                                                 Crust
                                                                                                 Outer core
                                                                                                 Inner core




       Crust (1 km):
 Little effect on the long term
 cooling. BUT: may contain                                                                                   C
                             A
 heating sources (magnetic/                     Neutron superfluid Neutron superfluid
 rotational, pycnonuclear under                                             +
                                                                  proton superconductor
                                                Neutron vortex
 accretion). Its thermal time is                                         Neutron vortex
 important for very young star                  Nuclei in a lattice Magnetic flux tube
 and for quasi-persistent accretion
                             “Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints”, Page D. & Reddy S., 2006ARNPS..56..327P

Dany Page      Thermal Behavior of Neutron Stars                     “Nuclear Matter at High Density”, Hirschegg, January 2009 43
            Dominant neutrino processes in the crust

            Plasmon decay process



      Bremsstrahlung processes:




        Pair annihilation process:


      Photo-neutrino process:




Dany Page      Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 44
            Early cooling of the crust (without pairing)




                                          All neutrino processes




Dany Page    Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 45
            Early cooling of the crust (without pairing)


                                   No plasma neutrinos




                                          All neutrino processes




Dany Page    Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 46
            Early cooling of the crust (without pairing)


                                   No plasma neutrinos


                                                     Only plasma
                                                      neutrinos



                                          All neutrino processes




Dany Page    Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 47
            Early cooling of the crust (without pairing)


                                   No plasma neutrinos

                                                                                       Plasma +
                                                     Only plasma                    bremsstrahlung:
                                                      neutrinos
                                                                                    e-e brem.
                                                                                    e-ion brem.
                                                                                    n-n brem.
                                          All neutrino processes




Dany Page    Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 48
              Effects of neutron                       1S
                                                         0       pairing (crust)


                                          No pairing (as previous case)




Dany Page   Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 49
              Effects of neutron                      1S
                                                        0       pairing (crust)




                             Only suppression
                               of neutron Cv :
                            shortens the thermal
                                 time-scale




Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 50
              Effects of neutron                       1S
                                                         0       pairing (crust)


                                                Suppression of Cv
                                                 and n-n brem.


                             Only suppression
                               of neutron Cv :
                            shortens the thermal
                                 time-scale




Dany Page   Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 51
              Effects of neutron                      1S
                                                        0       pairing (crust)




                               ... adding the PBF
                             neutrinos without vector
                             channel suppression ...




Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 52
              Effects of neutron                      1S
                                                        0       pairing (crust)


                                                   ... and with the vector
                                                    channel suppression




                               ... adding the PBF
                             neutrinos without vector
                             channel suppression ...




Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 53
            Effect of the size of the neutron                                       1S
                                                                                      0      gap


                                                 T




                                                                       Crust
                                                                       Core
                                                GC (?)




                                        CCDK    WAP
                                                          SFB




Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 54
            Effect of the size of the neutron                                       1S
                                                                                      0      gap


                                                         With the vector channel
                                                               suppression
                                                                             T
                                                                             GC (?)
                                                                             SFP
                                                                             WAP
                                                                             CCDK
                                  GC (?)
                                  T
                                   SFP
                                  WAP
                                 CCDK
                          Without the vector channel
                                suppression




Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 55
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                                             Sw



                                             La
                            Core:                                                                  Crust:
                                                                                                   nuclei
                     homogeneous                                                                     +
                          matter                                                                   neutron
                                                                                                   superfluid




                                                                                             Atmosphere
                                                                                             Envelope
                                                                                             Crust
                                                                                             Outer core
                                                                                             Inner core




                                                                                                Outer Core (10-x km):
                                                                                               Nuclear and supranuclear
                                                                                                     C
                                                                                               densities, containing n, p, e & µ.
                        A
                                            Neutron superfluid Neutron superfluid              Provides about 90% of cv and εν
                                                                        +
                                                              proton superconductor            unless an inner core is present.
                                            Neutron vortex
                                                                     Neutron vortex            Its physics is basically under
                                            Nuclei in a lattice Magnetic flux tube             control except pairing Tc which
                                                                                               is essentially unknown.
                         “Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints”, Page D. & Reddy S., 2006ARNPS..56..327P

Dany Page   Thermal Behavior of Neutron Stars                    “Nuclear Matter at High Density”, Hirschegg, January 2009 56
                                   Pairing Tc models

            Neutron 1S0                         Proton 1S0                       Neutron 3P2




                     Size and extent of pairing gaps is highly uncertain




Dany Page   Thermal Behavior of Neutron Stars     “Nuclear Matter at High Density”, Hirschegg, January 2009 57
                       PBF vs MURCA and Photons

            Neutron 3P2 gap “a”                 Neutron 3P2 gap “b”               Neutron 3P2 gap “c”




                                                                          Proton 1S0 from Amundsen & Ostgaard

Dany Page   Thermal Behavior of Neutron Stars         “Nuclear Matter at High Density”, Hirschegg, January 2009 58
            Effect of PBF without vector channel suppression



                                             Ligh
                                                 t ele
                                                      me
                                                          nt e
                                Hea                              nve
                                    vy e                            lope
                                         lem                               s
                                            ent
                                                    env
                                                         elop
                                                             es

                                Neutron 3P2 gap “a”
                               and the whole family of
                                 of 1S0 gaps (n & p)




                                Without vector channel suppression
Dany Page     Thermal Behavior of Neutron Stars            “Nuclear Matter at High Density”, Hirschegg, January 2009 59
            Effect of PBF with vector channel suppression



                                           Ligh
                                               t ele
                                                    me
                                                        nt e
                              Hea                              nve
                                  vy e                            lope
                                       lem                               s
                                          ent
                                                  env
                                                       elop
                                                           es

                              Neutron 3P2 gap “a”
                             and the whole family of
                               of 1S0 gaps (n & p)




                               With vector channel suppression
Dany Page   Thermal Behavior of Neutron Stars            “Nuclear Matter at High Density”, Hirschegg, January 2009 60
             Effect of vector channel suppression



                                           Ligh
                                               t ele
                                                    me
                                                        nt e
                              Hea                              nve
                                  vy e                            lope
                                       lem                               s
                                          ent
                                                  env
                                                       elop
                                                           es

                              Neutron 3P2 gap “a”
                             and the whole family of
                               of 1S0 gaps (n & p)




Dany Page   Thermal Behavior of Neutron Stars            “Nuclear Matter at High Density”, Hirschegg, January 2009 61
                                  Observational data




Dany Page   Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 62
                             Minimal Cooling versus data

 1. RX J0822-4247 (in SNR Puppis A)
 2. 1E 1207.4-5209 (in SNR PKS 1209-52)
 3. PSR 0538+2817                                                 Light elements
 4. RX J0002+6246 (in SNR CTB 1)                                     envelopes
 5. PSR 1706-44
 6. PSR 0833-45 (in SNR ``Vela'')
 7. PSR 1055-52                                                        A   0           1
                                                                                           2
 8. PSR 0656+14                                                                                     3
 9. PSR 0633+1748 (``Geminga'')
                                                      Heavy elements
                                                        envelopes                                       7
 10. RX J1856.5-3754                                                           C        4
                                                                           B           5                    8
 11. RX J0720.4--3125                                                                                            11
                                                                                                6
 0. PSR 0531+21(in Crab)                                                                    D
                                                                                   a                        10
 A. CXO J232327.8+584842 (in SNR Cas A)                                        b
 B. PSR J0205+6449 (in SNR 3C58)                                                   c                9
 C. PSR J1124--5916 (in SNR G292.0+1.8)
 D. RX J0007.0+7302 (in SNR CTA 1)                                             d

 a. ? (in SNR G315.4--2.3)
 b. ? (in SNR G093.3+6.9)
 c. ? (in SNR G084.2--0.8)
 d. ? (in SNR G127.1+0.5)




Dany Page         Thermal Behavior of Neutron Stars     “Nuclear Matter at High Density”, Hirschegg, January 2009 63
                  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




Dany Page   Thermal Behavior of Neutron Stars    “Nuclear Matter at High Density”, Hirschegg, January 2009 64
                      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




Dany Page      Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 65
                                                      tti
                                             Sp na
                                                   he
                                                  se
                                                                                   B




                                                   g
                                             ch iss




                                               ag
                                                sa
                                               ee
                                             Sw



                                             La
                            Core:                                                                  Crust:
                                                                                                   nuclei
                     homogeneous                                                                     +
                          matter                                                                   neutron
                                                                                                   superfluid




                                        Inner Core (x km ?):          Atmosphere
                                                                      Envelope
                                     The hypothetical region.         Crust
                                     Possibly only present in massive Outer core
                                     NSs. May contain Λ, Σ-, Σ0, π or Inner core
                                     K condensates, or/and
                                     deconfined quark matter. Its εν
                                     dominates the outer core by
                                     many orders of magnitude. Tc ?


                                                                                                         C
                        A
                                            Neutron superfluid Neutron superfluid
                                                                        +
                                                              proton superconductor
                                            Neutron vortex
                                                                     Neutron vortex
                                            Nuclei in a lattice Magnetic flux tube


                         “Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints”, Page D. & Reddy S., 2006ARNPS..56..327P

Dany Page   Thermal Behavior of Neutron Stars                    “Nuclear Matter at High Density”, Hirschegg, January 2009 66
                      Direct URCA with pairing vs data




       EOS: PAL
     Mcr = 1.35 MSun


      Pairing gaps:

   Neutron 1S0: “SFB”
    Neutron 3P2: “b”
    Proton 1S0: “T73”




Dany Page     Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 67
                         A “Maximal” cooling model (?)

                                                                                                   Comparison of two models
                                                                                                                with
                                                                                                          n, p & hyperons
                                                                                                        (DUURCA with Λ is
                                                                                                    controlled by its 1S0 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..85.2048P

Dany Page   Thermal Behavior of Neutron Stars                           “Nuclear Matter at High Density”, Hirschegg, January 2009 68
                      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




Dany Page      Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 69
                                   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.




Dany Page       Thermal Behavior of Neutron Stars   “Nuclear Matter at High Density”, Hirschegg, January 2009 70
                                           . . . 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 (?)

Dany Page       Thermal Behavior of Neutron Stars     “Nuclear Matter at High Density”, Hirschegg, January 2009 71
72

				
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