Superfluid Heat Conduction in the Neutron Star Crust

Transcription

1 Superfluid Heat Conduction in the Neutron Star Crust Sanjay Reddy Los Alamos National Lab Collaborators : Deborah Aguilera Vincenzo Cirigliano Jose Pons Rishi Sharma arxiv:

2 Thermal Conduction 101 C electron n e ( T E F ) C Phonon T 3 v 3 s Electrons dominate transport in conductors: C electron v F C Phonon v s k2 F T 2 v2 s In insulators lattice phonons dominate. Their conduction can be large since phonon mean free paths are typically large.

3 Electrons or Phonons? Typically electrons dominate - unless there is a large magnetic field. Magnetic field suppresses transverse conduction =Gyrofrequency = Collision time Canuto and Ventura (1977) Uripin & Yakovlev (1980)

4 Electrons or Phonons? Typically electrons dominate - unless there is a large magnetic field. Magnetic field suppresses transverse conduction =Gyrofrequency = Collision time Canuto and Ventura (1977) Uripin & Yakovlev (1980)

5 Phonon Conduction in the Outer Crust Lattice Phonons have large mean free paths. Mean free path set by: 1.Impurity scattering 2.Absorption by Electrons Perez-Azorin (2006) Chugunov and Haensel (2007)

6 Phonon Conduction in the Outer Crust Lattice Phonons have large mean free paths. Mean free path set by: 1.Impurity scattering 2.Absorption by Electrons Impurity Scattering Perez-Azorin (2006) Chugunov and Haensel (2007)

7 Phonon Conduction in the Outer Crust Lattice Phonons have large mean free paths. Mean free path set by: 1.Impurity scattering 2.Absorption by Electrons Impurity Scattering Electron Absorption Perez-Azorin (2006) Chugunov and Haensel (2007)

8 Phonon Conduction in the Outer Crust Lattice Phonons have large mean free paths. Mean free path set by: 1.Impurity scattering 2.Absorption by Electrons Impurity Scattering Electron Absorption Perez-Azorin (2006) Chugunov and Haensel (2007)

9 Superfluidity in the Crust Enhances Heat Conduction: Conventional Wisdom: Electrons dominate conduction At neutron drip and T=10 8 K

10 Superfluidity in the Crust Enhances Heat Conduction: Conventional Wisdom: Electrons dominate conduction At neutron drip and T=10 8 K At B = G

11 Superfluidity in the Crust Enhances Heat Conduction: Conventional Wisdom: Electrons dominate conduction At neutron drip and T=10 8 K At B = G

12 Heat Transport in the Inner Crust Neutron matter in the crust is superfluid. Neutron particle-hole excitations are gapped Δ (MeV) k F [fm -1 ] BCS Chen [26] Wambach [27] Schulze [28] Schwenk [29] Fabrocini [30] AFDMC [30] QMC k F a Gezerlis & Carlson (2008) Low energy degrees of freedom: 1.Electrons 2.Lattice Phonons (1 long. + 2 Trans.) 3.Superfluid Phonons

13 Dissipative Processes Electrons lphs sphs Electron-phonon processes Impurity (Rayleigh) scattering Multi electron and phonon processes

14 Dissipative Processes Electrons lphs sphs Electron-phonon processes Impurity (Rayleigh) scattering Multi electron and phonon processes

15 sph mean free path Rayleigh Scattering ro =Typical nuclear radii q = sph momentum Scattering dominated by impurities: Very large mean free path! If only impurity scattering is relevant:

16 Low Energy Theory Phonon coupling is derivative - Low momentum phonons interact weakly!

17 Low Energy Theory Phonon coupling is derivative - Low momentum phonons interact weakly! kinetic terms

18 Low Energy Theory Phonon coupling is derivative - Low momentum phonons interact weakly! kinetic terms coupling to Fermions

19 Low Energy Theory Phonon coupling is derivative - Low momentum phonons interact weakly! kinetic terms coupling to Fermions self-coupling

20 Low Energy Theory Phonon coupling is derivative - Low momentum phonons interact weakly! kinetic terms coupling to Fermions self-coupling

21 Low Energy Theory Phonon coupling is derivative - Low momentum phonons interact weakly! kinetic terms coupling to Fermions self-coupling lph-sph mixing

22 Low Energy Theory Phonon coupling is derivative - Low momentum phonons interact weakly! kinetic terms coupling to Fermions self-coupling lph-sph mixing sph 2 lph

23 Electron-Phonon Coupling Fetter & Walecka

24 Electron-Phonon Coupling Fetter & Walecka Fluctuation in density due to displacement field :

25 Electron-Phonon Coupling Fetter & Walecka Fluctuation in density due to displacement field : Canonically normalized lattice phonon field

26 Electron-Phonon Coupling Fetter & Walecka Fluctuation in density due to displacement field : Canonically normalized lattice phonon field

27 Electron-Phonon Coupling Fetter & Walecka Fluctuation in density due to displacement field : Canonically normalized lattice phonon field

28 Neutron-lPh Interaction Low-energy neutron-nucleus potential (Fermi Potential)

29 Neutron-lPh Interaction Low-energy neutron-nucleus potential (Fermi Potential)

30 Neutron-lPh Interaction Low-energy neutron-nucleus potential (Fermi Potential)

31 Neutron-lPh Interaction Low-energy neutron-nucleus potential (Fermi Potential)

32 sph-lph Interactions Integrate-out neutron degree of freedom

33 sph-lph Interactions Integrate-out neutron degree of freedom In the neutron star crust:

34 sph-lph Interactions Integrate-out neutron degree of freedom In the neutron star crust: Now we are ready to calculate the sph mean free path

35 Mixing and Dissipation Mixing leads to oscillations Dissipation of lph leads to dissipation of sph

36 Mixing and Dissipation Mixing leads to oscillations Dissipation of lph leads to dissipation of sph

37 Mixing and Dissipation Mixing leads to oscillations Dissipation of lph leads to dissipation of sph sph mean free path lph mean free path

38 Mixing and Dissipation Mixing leads to oscillations Dissipation of lph leads to dissipation of sph sph mean free path lph mean free path

39 Mixing and Dissipation Mixing leads to oscillations Dissipation of lph leads to dissipation of sph sph mean free path lph mean free path Away from resonance

40 Superfluid Phonon Mean Free Path λ sph ( ω=3 T) cm T=10 8 K T=10 7 K T=10 6 K ρ (g/cm 3 )

41 Superfluid Phonon Mean Free Path λ sph ( ω=3 T) cm T=10 8 K T=10 7 K T=10 6 K neutron-drip ρ (g/cm 3 )

42 Superfluid Phonon Mean Free Path λ sph ( ω=3 T) cm T=10 8 K T=10 7 K T=10 6 K resonance neutron-drip ρ (g/cm 3 )

43 Thermal Conductivity

44 Consequences for Magnetar Cooling Surface temperature anisotropy due anisotropic conduction. θ sph can limit the anisotropy

45 Very Large Magnetic Fields - Dissipation Electrons are in a few Landau levels. Transitions are highly restricted. Anisotropic dissipation. Phonon propagation is nearly undamped in many directions. As the energy - momentum conservation is satisfied over a small range of angles. Sharma & Reddy (2009) in prep

46 Very Large Magnetic Fields - Screening Electrons screen ionion interactions. The screening length is sensitive to B for 1000 large B. B= G B=0 V (r) = Z2 e 2 g(r) r ( g(r) = exp r ) λ D λ D (fm) µ e (MeV) Sharma & Reddy (2009) in prep

47 Very Large Magnetic Fields - Screening Electrons screen ionion interactions. The screening length Friedel Oscillations is sensitive to B for 1000 large B. B= G B=0 Typically Friedel V (r) = Z2 e 2 oscillations are small g(r) r in the relativistic ( g(r) = exp r ) systems - but large B suppresses kf. λ D λ D (fm) µ e (MeV) Sharma & Reddy (2009) in prep

48 Conclusions New mode for heat conduction in the inner crust. Low energy EFT for sphs, lphs and electrons. sph conduction is likely to be important for thermal evolution of magnetars. Screening and Friedel oscillations can affect the mechanical structure and phase structure of the magnetar outer crusts.

49 Electron Thermal Conduction Electrons are degenerate & relativistic Electron mean free path set by collisions with ions. Energy transfer ~ T Momentum transfer ~ kfe

50 Neutron-Nucleus Interaction In medium Pauli blocking and effective range corrections can suppress the interaction.

51 Electron Scattering and the Dynamic Structure Factor Coulomb Logarithm Flowers & Itoh (1976) Yakovlev & Urpin (1980) Potekhin et al. (1999) Dynamic Structure Factor

52 Potekhin (1999) Plasma physics of the outer crust: Γ = Z2 e 2 Γ c 175 a kt ( ) 1/3 A 1 a 125 fm 50 ρ 10 kt = T 10 8 K fm 1