Shear viscosity due to phonons in superfluid neutron stars

Abstract

We compute the contribution of phonons to the shear viscosity $\eta$ in superfluid neutron stars, assuming neutron pairing in a ${}^1{S}_0$ channel. We use a Boltzmann equation amended by a collision term that takes into account the binary collisions of phonons. We use effective field theory techniques to extract the phonon scattering rates, written as a function of the equation of state (EoS) of the system. Our formulation is rather general, and can be used to extract the shear viscosity due to binary collisions of phonons for other superfluids, such as the cold Fermi gas in the unitarity limit. We find that $\eta \propto 1/T^5$, the proportionality factor depending on the EoS of the system. Our results indicate that the phonon contribution to $\eta$ cannot be ignored and might have relevant effects in the dynamics of the different oscillation modes of the star.

13 pages; a new curve added; to be published in PRD

References in corpus (6)

• Theory of ultracold Fermi gases
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Shear viscosity of a superfluid Fermi gas in the unitarity limit
• Low-Energy Quantum Effective Action for Relativistic Superfluids
• Superfluid Heat Conduction and the Cooling of Magnetized Neutron Stars
• A low energy theory for superfluid and solid matter and its application to the neutron star crust

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