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

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

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-dot diagram of pulsars. 3.2 Shear viscosity. In-medium pions for bulk viscosity. 3.3 Layered neutron star

Nucleon-nucleon interaction 1 2 r p1 p2 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 +

QCD with light quarks

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

PIONIZATION OF THE NEUTRON STAR MATTER

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

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)

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

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

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)

P-WAVE PION CONDENSATION

Baym Migdal Scalapino 1974 Tbilisi

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

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

THE FERMI-LIQUID THEORY PION CONDENSATION WITHIN THE FERMI-LIQUID THEORY

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

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 ?

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

Solutions for zeroth harmonics keep only zeroth harmonics Lindhard function

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

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

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

Spin channel pure neutron matter similar solutions as 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

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

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

Nucleon-nucleon interaction in dense matter based on a separation of long and short scales full pion propagator: enhancement of the amplitude dressed vertex: suppression 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]

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)]

Green’s functions only 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

NEUTRON STAR COOLING

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 initial period current period 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

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

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]

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

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

EoS should produce a large DU threshold in NS matter ! 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]

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

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

R-MODES IN NEUTRON STARS

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.

Rossby waves on Earth: in oceans and atmosphere The returning force for these wave is the Coriolis force Carl-Gustaf Rossby

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

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.

R-mode is unstable if the time >0 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

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

Lepton shear viscosity Lepton shear viscosity = electron + muon contribution low T, Fermi liquid results Lepton collision time tl is 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

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

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]

Neutrino shear viscosity With the temperature increase the neutrino mean free path decreases and for sufficiently high temperatures neutrinos become trapped inside the neutron star interior. Neutrino mean free path is determined by inverse MMU and PU processes weak T dependence contributes only in regions where neutrinos are trapped opacity radius is determined as

Lepton shear viscosity

nucleon relaxation time; Bulk viscosity collisional [Sykes, Brooker, Ann. Phys. 56(1970) 1] F0 is the zeroth harmonics of the dimensionless scalar Landau-Migdal parameter, F0~ 1 nucleon relaxation time; small contribution

Energy dissipation of the mode: is neutrino emissivity Bulk viscosity Energy dissipation of the mode: is neutrino emissivity Energy of the mode decreases if the pressure depends on an order parameter, which variation is delayed with respect to the variation of the density [Mandelstam, Leontovich, ZhETF 7(1937)438] soft mode [Sawyer PRD39, Haensel, Levenfish, Yakovlev A&A357, A&A372] order parameter is lepton concentration relaxation time average over the perturbation period

[calculated with FOPE] or medium MU (MMU) [calculated with MOPE]; for sum over various processes changing dXl direct Urca (DU); modified Urca (MU) [calculated with FOPE] or medium MU (MMU) [calculated with MOPE]; pion condensate Urca (PU)

Shear and bulk viscosities. Results MMU+DU

R-mode stability window shear bulk

Young pulsars 1. star is born hot and rapidly rotating (point A) 2. cooling time (heat transport!) >> spin-down time for max. r-mode amplitude 3. star moves along line AB because of r-modes 4. line BC, cooling and magnetic breaking Minimum point B must be above 62 Hz (PSRJ0537-6910)

Minimum of the stability window

LMXB recycled pulsars Rotation of LMXB pulsars cannot be explained. Shear viscosity is too small. Alternative mechanisms differential drift in magnetic field [Rezzolla, Lamb, Shapiro] -weak reactions with hyperons +hyperon pairing [Jones; Nayyar Owen] core-crust coupling [Bildsten, Ushomirsky, Levin] saturation of r-mode amplitude at small values [Arras, Bondaresku, Wasserman] non-linear decay of r-modes [Kastaun] coupling to more stable modes [Gusakov, Chugunov, Kantor] -vortex flux-tube interactions [Haskell, Glampedakis, Andersson]

Soft bosonic modes in rapidly rotating systems dispersion laws of the low-lying bosonic excitations zero-sounds in normal fermionic system AB, Carlson-Goldman in fermionic superfluid pion and kaon p-wave condensates What happens if the medium flows with a velocity v>vc? [Pitaevskii ’84; Voskresenky 93;Baym, Pethick 12] There appears a Bose condensate of excitations, which will carry a part of the momentum and the fluid will move with smaller velocity. differential rotation of the star

Outer part of the core does not rotates. Crust rotates Minimal rc is determined by the size of the proton paring zone

Pion in neutron star, to be or not to be? Conclusions Pion in neutron star, to be or not to be? pionization? NO! p-wave pion condensation. Yes!? But (g’ short-range correlations?, mN*) 2. Neutron star cooling medium “Modified Urca” – a mechanism to understand NS cooling 3. R-modes and viscosity of NS matter moderate increase nucleon shear viscosity for small NS masses partial trapping of neutrinos in the star core at T~2x109 – 1010 K large neutrino shear viscosity for T>2x109 strong increase of the bulk viscosity

STAR MODEL

Neutron star model HDD EoS n,p,e,m, matter [Blaschke, Grigorian, Voskresensky, PRC 88 (13) 065805] based on Heiselberg-Hjorth-Jensen (HHJ) analytical parameterization of the microscopic Akmal-Pandharipande-Ravenhall (APR) EoS with A18+ dv+U IX* forces n,p,e,m, matter binding energy per nucleon: scaling function: The scaling function makes EoS harder for n>5n0, but the EoS remains causal.

HDD EoS Friedman-Pandharipande-Skyrme EoS mass and radius proton and electron concentration thresholds of Direct Urca reactions thresholds of Modified Urca reactions on protons density profiles similar to the Tolman V solution

1S0 neutron and proton pairing parameterizations from [Kaminker, Yakovlev, Gnedin, A&A383(2002)1076] motivated by the calculations of Wambach, Ainsworth, Pines (1993) and Schulze, Cugnon, Lejeune, Baldo, Lombardo (1996) including in-medium modifications of the NN interaction BCS calculations with vacuum interaction, Vlow-k [Hebeler, Schwenk, Friman, PLB 648 (2007) 176] 3P2 neutron pairing [Schwenk, Friman, PR92 (2004) 082501 (2004)] triplet paring is supperessed by medium-induced spin-orbit interaction. [Ding, Witte, Dickhoff, Dussan, Rios, Polls, arXiv:1406.7789] long-range density and spin fluctuations preclude triplet pairing We will ignore triplet pairing

Profiles of critical temperatures for the singlet neutron and proton pairing