Shear viscosity and the r-mode instability window in superfluid neutron stars

TL;DR

This paper investigates how superfluid phonons and electron collisions influence shear viscosity and the r-mode instability window in neutron stars, revealing that phonons dominate at high temperatures and differ from previous models.

Contribution

It provides a new analysis of shear viscosity contributions from superfluid phonons and electron collisions, offering updated insights into the r-mode instability window in neutron stars.

Findings

Superfluid phonons dominate shear viscosity at high temperatures.

The r-mode instability window differs from previous models.

Electron collisions contribute significantly to shear viscosity at lower temperatures.

Abstract

We analyze how recent computations of the shear viscosity $\eta$ in the core of superfluid neutron stars affect the r-mode instability window. We first analyze the contribution of superfluid phonons to the viscosity, both in their hydrodynamical and ballistic regime. We also consider the recent computation of $\eta$ arising from the collisions of electrons with electrons and protons by Shternin and Yakovlev, and discuss how the interactions among superfluid phonons and electrons might contribute to the shear viscosity. For assessing the r-mode instability window we compare the shear viscosity due to phonons in the hydrodynamical regime with respect to the shear viscosity due to electron collisions. Only at high temperatures the superfluid phonon contribution to $\eta$ starts to dominate the process of r-mode damping. While our results for the instability window are preliminary, as other dissipative processes should be taken into account as well, they differ from previous evaluations of the r-mode damping due to the shear viscosity in superfluid neutron stars.