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Pions in Neutron Stars

Pions, Neutron stars, Pionization, P-wave pion condensation, Neutron star cooling, R-modes, Viscosity, Nucleon-nucleon interaction

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Pions in Neutron Stars

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  1. Pions in Neutron Stars Evgeni E. Kolomeitsev (Matej Bel University, Banska Bystrica, Slovakia LTP, JINR, Dubna, Russia )

  2. Hideki Yukawa 1935 proposed a quantum of strong interactions 1940 professor in Kyoto University 1949 Nobel Prize in Physics 1953 the first chairman of YITP

  3. Pion in neutron star, to be or not to be? 1.1 Pionization. Chiral shield against it 1.2 P-wave pion condensation. Short-range correlations 2. Neutron star cooling 2.1 “Modified Urca” reactions (dynamical pions) 2.2 Medium “Modified Urca” – a mechanism to understand NS cooling 3. R-modes and viscosity of NS matter 3.1 R(Rossby)-mode instability. Age-P-dotdiagramofpulsars. 3.2 Shearviscosity. In-mediumpionsforbulkviscosity. 3.3 Layered neutron star

  4. 2 p2 r p1 1 Nucleon-nucleon interaction several scales are involved non-relativistic description vector mesons:mw,r~800 MeV , r~0.24 fm correlated 2¼ exchange: m~200-600 MeV r~0.3—1fm 1-pion exchange: m¼=140 MeV r~1.4 fm relativistic description + Equilibrium density of an atomic nucleus n0=0.16 fm-3 inter-nuclear distance (n0)-1/3=1.8 fm

  5. QCD with light quarks

  6. gradient couplings expansion in small pion momenta and masses (½+) parity partners (½-) Pions – Goldstone bosons of chiral symmetry breaking chiral gap

  7. PIONIZATION OF THE NEUTRON STAR MATTER

  8. Equation of state of nuclear matter symmetry energy There is a correlation among parameters: J, L, Ksym

  9. If we assume some model for the density dependence of the symmetry energy Analysis of 36 RMF models gives [Dong, et al PRC85, 034308 (2012)] More details and other relations in Tews, Lattimer et al, ApJ848, 105(2017)

  10. Weak reactions start Simple model for NS matter n+p+e+m matter Lightest negatively charged bosons: p- minimum at k=0 Pionization of neutron star matter

  11. Weinberg Tomazawa theorem Chiral symmetry for pion-nucleon interaction isospin even and odd amplitudes Chiral symmetry: for forward scattering amplitude: repulsive in neutron reach matter

  12. chiral shield against pionization 29 MeV<J<38 MeV Detailed analysis of the possibility of the s-wave pion condensation in Onishi, Jido et al, PRC 80, 038202 (2009)

  13. P-WAVE PION CONDENSATION

  14. Baym Migdal Scalapino 1974 Tbilisi

  15. Tensor forces in NN interaction Resummed, enhanced pion exchange nucleon arrangement

  16. Alternating-layer-spin configurations Ryozo Tamagaki Tatsuyuki Takatsuka 1972’-73’ p0 condensate tensor force contribution to the energy

  17. PION CONDENSATION WITHIN THE FERMI-LIQUID THEORY

  18. Fermi liquid theory system of strongly interacting fermions (no pairing) single-particle excitation mechanism quasiparticle n n’ particle-hole interaction on Fermi surface short-range long-range particle-hole propagator pole parts Landau parameters

  19. density of states at the Fermi surface number of fermion types neutron matter: (1 parameter in each channel) nuclear matter: (3 parameters in each channel) In matter of arbitrary isospin composition these parameters are independent. Fermi-liquid renormalization is different for these parameters. small isospin disballance (2 parameters in each channel) In nuclear physics one uses also the normalization on the nuclear Fermi surface constant, independent of density Density dependence? Residual momentum dependence ?

  20. effective mass compressibility symmetry energy There are relations between some Landau parameters and bulk properties of the system In general Landau parameter are to be fitted to empirical information (nucleus properties)

  21. Solutions for zeroth harmonics keep only zeroth harmonics Lindhard function

  22. Lindhard function Imaginary part Results of expansions depends on the expansion order: Temperature corrections

  23. Landau damping Scalar modes zero-sound modes I. II. “diffuson” stable mode unstable mode III.

  24. pion with residual (irreducible in NN-1 and  N-1) s-wave  N interaction and  scattering`` Fermi-liquid with pions Part of the interaction involving  isobar is analogously constructed:

  25. Spin channel pure neutron matter Consider now the spin channel include the pion exchange explicitly similar solutions as in scalar channel s-wave and D parts of polarization operator pion nucleon coupling constant If there is a “diffuson” solution Can change the sign at some momentum and density! Instability: pion condensation

  26. Critical density of pion condensation Without short-range correlations (g’) the critical density of the pion condensation would be 0.3 n0!

  27. Spectrum of diffusive pion mode We search for a diffusive solution roton-like spectrum effective pion gap

  28. full pion propagator: enhancement of the amplitude dressed vertex: suppression Nucleon-nucleon interaction in dense matter based on a separation of long and short scales Similar to Debye screening in plasma Landau-Migdal parameters of short-range interaction are extracted from atomic nuclei Poles yield zero-sound modes in scalar and spin channels known phenomena in Fermi liquid provided short-scale interaction can be reduced to the local one [Migdal et al., Phys. Rep. 192 (1990) 179]

  29. pion propagator for pion gap reconstruction of pion spectrum on top of the pion condensate LM parameters increase with density saturation of pion softenning no pion condensate amplitude of the pion condensate [Migdal, Rev.Mod. Phys. 50 (1978), Migdal, Sapershtein,Troitsky, Voskresensky Phys. Rept. 192 (1990)]

  30. Vertex renormalization in FL Coupling of an external field to a particle pole parts of Green’s functions only “bare” (FL renormalized) vertex Effects: Reduce couplings. “A shield” against pion condensation Produce sound modes contributing to response functions Enhance reactions in some channels

  31. NEUTRON STAR COOLING

  32. initial period current period Pulsar age Pulsar rotation period/frequency changes with time: e.m. wave emission grav. wave emission • angle between rotation a and magnetic axes e neutron star eccentricity spin-down age: braking index: kinematic age: 3) historical events 1) age of the associated SNR Crab : 1054 AD Cassiopeia A: 1680 AD Tycho’s SN: 1572 AD 2) pulsar speed and position w.r. to the geometric center of the associated SNR

  33. Given: • EoS • Cooling scenario[neutrino production] Mass of NS Cooling curve

  34. Neutron Star Cooling Data 3 groups: >103 in emissivity slow cooling intermediate cooling rapid cooling All groups can be described within one cooling scenario if there is a strong dependence of neutrino luminocity on the NS mass strong density-dependence of emissivity [Voskresensky, Senatorov 1986]

  35. emissivity Neutrino emission reactions neutron star is transparent for neutrino CV – heat capacity, L - luminosity each leg on a Fermi surface /T neutrino phase space ´ neutrino energy

  36. pair formation-breaking process (PFB) standard modified Urca(MU) exotic Direct Urca(DU) Direct Urca on pion(PU)

  37. DU process schould be „exotics“(if DU starts it is dificult to stop it) [Blaschke, Grigorian, Voskresensky A&A 424 (2004) 979] EoS should produce a large DU threshold in NS matter ! [EEK, Voskresensky NPA759 (2005) 373]

  38. enhancement factors w.r.t. MU emissivity medium MU reactions medium bremsstrahlung reactions vertex correlation function

  39. Neutron star cooling [Blaschke, Grigorian, Voskresensky PRC88 (2013)065805]

  40. R-MODES IN NEUTRON STARS

  41. Age-period diagram for pulsars The ATNF pulsar catalogue recycled pulsars stability of old pulsars? Young pulsars periods are much larger than the Kepler limit.

  42. Rossby waveson Earth: in oceans and atmosphere The returning force for these wave is the Coriolis force Carl-Gustaf Rossby

  43. R-mode instability of rotating neutron star and viscosity In a superdense system like a neutron star the Rossby waves are sources of gravitational radiation. 1998 it was shown by Andersson, Friedman and Morsnik showed that this radiation leads to an increase of the amplitude of the mode. so there is an instability Large R-modes can either destroy the star or the star stop rotating Viscosity of the dense nuclear matter can damp r-modes and save the rotating star

  44. R-modes in rotating neutron star Consider a neutron star with a radius R rotating with a rotation frequency W and a perturbation in the form oscillation amplitude oscillation frequency (dominant modes for l=m=2) for a<<1 amplitude changes viscous damping [Andersson ApJ 502 (98) 708; Friedman, Morsink, ApJ 502 (98) 714] gravitational radiation drives r-mode unstable [Lindblom, Owen, Morsink, PRL80 (98) 4843] If the r-modes are undamped, the star would lose its angular moment on the time scale of tG, because of an enhanced emission of gravitation waves.

  45. R-modes stability R-mode is unstable if the time >0 gravitational time scale damping rate due to the shear viscosity damping rate due to the bulk viscosity [Lindblom, Owen, Morsnik PRL 80 (98) 4843 Owen, Lindblom, Cutler, Schutz, Vecchio, Andersen PRD58 (98) 084020] profile averages

  46. Viscosity Euler equation: shear viscosity bulk viscosity Dissipation after uniform volume change Dissipation when there is a velocity gradient Maxwell (1860) kinetic theory calculations Units: (naïve estimate) Nuclear matter:

  47. Lepton shear viscosity Lepton shear viscosity = electron + muon contribution low T, Fermi liquid results Lepton collision timetlis determine by lepton-lepton and lepton-proton collisions 1979 Flowers and Itoh: Important role of the phonon modification (plasmon exchange) for QCD plasma [Heiselberg, Pethick Phys. Rev.D 48 (1993)2916] [Shternin, Yakovlev, Phys. Rev. D 78 (2008) 063006] leading terms for small T muon contributions are important

  48. Effects of proton pairing on lepton shear viscosity Lepton shear viscosity vs. neutron star mass [Shternin, Yakovlev, Phys. Rev. D 78 (2008) 063006]

  49. Nucleon shear viscosity Fermi liquid result [Shternin, Yakovlev, Phys. Rev. D 78 (2008) 063006] effective NN cross section FOPE: MOPE: modification factor [Bacca et al, PRC80]

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