Dissipation in relativistic superfluid neutron stars

TL;DR

This paper develops a comprehensive framework for analyzing the damping of oscillations in relativistic superfluid neutron stars, incorporating finite temperature effects and mode coupling, with implications for neutron star thermal evolution.

Contribution

It extends the decoupling method for superfluid and normal modes to finite temperatures and derives general formulas for damping times applicable to all oscillation modes.

Findings

Ordinary one-fluid hydrodynamics approximates normal f-mode damping times at most temperatures.

Approximation is poor for radial and p-modes.

Resonance coupling causes rapid changes in damping times during thermal evolution.

Abstract

We analyze damping of oscillations of general relativistic superfluid neutron stars. To this aim we extend the method of decoupling of superfluid and normal oscillation modes first suggested in [Gusakov & Kantor PRD 83, 081304(R) (2011)]. All calculations are made self-consistently within the finite temperature superfluid hydrodynamics. The general analytic formulas are derived for damping times due to the shear and bulk viscosities. These formulas describe both normal and superfluid neutron stars and are valid for oscillation modes of arbitrary multipolarity. We show that: (i) use of the ordinary one-fluid hydrodynamics is a good approximation, for most of the stellar temperatures, if one is interested in calculation of the damping times of normal f-modes; (ii) for radial and p-modes such an approximation is poor; (iii) the temperature dependence of damping times undergoes a set of rapid changes associated with resonance coupling of neighboring oscillation modes. The latter effect can substantially accelerate viscous damping of normal modes in certain stages of neutron-star thermal evolution.