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Title: Transport coefficients in superfluid neutron stars

Abstract

We study the shear and bulk viscosity coefficients as well as the thermal conductivity as arising from the collisions among phonons in superfluid neutron stars. We use effective field theory techniques to extract the allowed phonon collisional processes, written as a function of the equation of state and the gap of the system. The shear viscosity due to phonon scattering is compared to calculations of that coming from electron collisions. We also comment on the possible consequences for r-mode damping in superfluid neutron stars. Moreover, we find that phonon collisions give the leading contribution to the bulk viscosities in the core of the neutron stars. We finally obtain a temperature-independent thermal conductivity from phonon collisions and compare it with the electron-muon thermal conductivity in superfluid neutron stars.

Authors:
 [1];  [2];  [1];  [3];  [4]
  1. Instituto de Ciencias del Espacio (IEEC/CSIC) Campus Universitat Autònoma de Barcelona, Facultat de Ciències, Torre C5, E-08193 Bellaterra (Barcelona) (Spain)
  2. (Germany)
  3. Tata Institute of Fundamental Research, Homi Bhaba Road, Mumbai-400005 (India)
  4. Physik Department, Technische Universität München, D-85748 Garching (Germany)
Publication Date:
OSTI Identifier:
22499078
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1701; Journal Issue: 1; Conference: 11. conference on quark confinement and hadron spectrum, Saint Petersburg (Russian Federation), 8-12 Sep 2014; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; DAMPING; ELECTRON COLLISIONS; ELECTRONS; EQUATIONS OF STATE; FIELD THEORIES; MUONS; NEUTRON STARS; PHONONS; SCATTERING; SHEAR; SUPERFLUIDITY; THERMAL CONDUCTIVITY; VISCOSITY

Citation Formats

Tolos, Laura, Frankfurt Institute for Advances Studies. Johann Wolfgang Goethe University, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main, Manuel, Cristina, Sarkar, Sreemoyee, and Tarrus, Jaume. Transport coefficients in superfluid neutron stars. United States: N. p., 2016. Web. doi:10.1063/1.4938690.
Tolos, Laura, Frankfurt Institute for Advances Studies. Johann Wolfgang Goethe University, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main, Manuel, Cristina, Sarkar, Sreemoyee, & Tarrus, Jaume. Transport coefficients in superfluid neutron stars. United States. doi:10.1063/1.4938690.
Tolos, Laura, Frankfurt Institute for Advances Studies. Johann Wolfgang Goethe University, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main, Manuel, Cristina, Sarkar, Sreemoyee, and Tarrus, Jaume. 2016. "Transport coefficients in superfluid neutron stars". United States. doi:10.1063/1.4938690.
@article{osti_22499078,
title = {Transport coefficients in superfluid neutron stars},
author = {Tolos, Laura and Frankfurt Institute for Advances Studies. Johann Wolfgang Goethe University, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main and Manuel, Cristina and Sarkar, Sreemoyee and Tarrus, Jaume},
abstractNote = {We study the shear and bulk viscosity coefficients as well as the thermal conductivity as arising from the collisions among phonons in superfluid neutron stars. We use effective field theory techniques to extract the allowed phonon collisional processes, written as a function of the equation of state and the gap of the system. The shear viscosity due to phonon scattering is compared to calculations of that coming from electron collisions. We also comment on the possible consequences for r-mode damping in superfluid neutron stars. Moreover, we find that phonon collisions give the leading contribution to the bulk viscosities in the core of the neutron stars. We finally obtain a temperature-independent thermal conductivity from phonon collisions and compare it with the electron-muon thermal conductivity in superfluid neutron stars.},
doi = {10.1063/1.4938690},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1701,
place = {United States},
year = 2016,
month = 1
}
  • We calculate the three bulk viscosity coefficients as arising from the collisions among phonons in superfluid neutron stars. We use effective field theory techniques to extract the allowed phonon collisional processes, written as a function of the equation of state of the system. The solution of the dynamical evolution of the phonon number density allows us to calculate the bulk viscosity coefficients as function of the phonon collisional rate and the phonon dispersion law, which depends on the neutron pairing gap. Our method of computation is rather general, and could be used for different superfluid systems, provided they share themore » same underlying symmetries. We find that the behavior with temperature of the bulk viscosity coefficients is dominated by the contributions coming from the collinear regime of the 2↔3 phonon processes. For typical star radial pulsation frequencies of ω ∼ 10{sup 4}s{sup −1}, we obtain that the bulk viscosity coefficients at densities n∼>4n{sub 0} are within 10% from its static value for T∼<10{sup 9} K and for the case of strong neutron superfluidity in the core with a maximum value of the {sup 3}P{sub 2} gap above 1 MeV, while, otherwise, the static solution is not a valid approximation to the bulk viscosity coefficients. Compared to previous results from Urca and modified Urca reactions, we conclude that at T ∼ 10{sup 9}K phonon collisions give the leading contribution to the bulk viscosities in the core of the neutron stars, except for n ∼ 2n{sub 0} when the opening of the Urca processes takes place.« less
  • Transport properties of a strongly interacting superfluid mixture of two Fermi liquids are studied. A typical example of such matter is the neutron-proton liquid in the cores of neutron stars. To describe the mixture, the Landau theory of Fermi liquids, generalized to allow for the effects of superfluidity, is employed. The kinetic equation is formulated and the linear response of the system to vector (e.g., electromagnetic) perturbation is analyzed. In particular, the transverse and longitudinal polarization functions for both liquid components are calculated. It is demonstrated that they can be expressed through the Landau parameters of the mixture and polarizationmore » functions of noninteracting matter (when the Landau quasiparticle interaction is neglected). These results can be used, for example, for studies of the kinetic coefficients and low-frequency long-wavelength collective modes in superfluid Fermi mixtures.« less
  • Time correlation functions for the transport coefficients in the linear Landau-Khalatnikov equations are derived on the basis of a formal theory. These Green--Kubo expressions are then explicitly evaluated for a dilute superfluid and the resulting transport coefficiencts are shown to be identical to those obtained previously by using a distribution function method.
  • We explore the consequences of a phenomenological model for the low-frequency interaction (vertex function) in /sup 3/He of the form GAMMA/sup k/ approx.-J (q) S x S + V (q). Here q represents the magnitude of the momentum and energy transfer. This is the second in a series of two papers and is concerned primarily with transport properties and the superfluid free energy. In the first paper we demonstrated that for spin-fluctuation-like models, in which J is peaked at q = 0 and V is relatively small, we obtain good agreement between theory and experiment for the magnitude and pressuremore » dependence of the superfluid transition temperature. In the present paper we show that these spin-fluctuation-like models yield reasonably good agreement with the measured zero-temperature transport coefficients at all pressures. They, therefore, represent a considerably better description of the high-pressure scattering amplitudes than the s-p approximation. The five fourth-order superfluid Landau-Ginzburg free-energy invariants, ..beta../sub i/, are computed using the Ranier-Serene formalism. At high and low pressures, paramagnonlike theories yield results essentially equivalent to those obtained in the s-p approximation. As in all previous calculations, while the combination ..beta../sub 2/ + ..beta../sub 4/ is in nearly exact agreement with high-pressure data, vertical-bar ..beta../sub 5/ vertical-bar is about 30% too large. We have also considered models for GAMMA/sup k/ in which J is of the spin-density wave form and in which J = 0. In both these cases the transport coefficients and the ..beta../sub i/ are inconsistent with experiment. The evidence strongly suggests that it is the proximity to the ferromagnetic instability which governs the behavior of the scattering amplitudes in /sup 3/He and all properties derived from them.« less
  • The neutrons inside neutron stars are almost certainly superfluid below a critical temperature T/subc/approx.10/sup 10/ K. Below T/subc/, pairs of excited neutron quasiparticles may recombine, resulting, if weak neutral currents exist, in the emission of neutrino-antineutrino pairs. We calculate the emissivity associated with this process and compare it with other neutrino emissivities. For neutron star interior temperatures in the range 10/sup 9/-10/sup 10/ K the recombination emissivity can dominate all others. (AIP)