Relativistic r-modes and shear viscosity

TL;DR

This paper derives relativistic equations for stellar perturbations including shear viscosity, numerically analyzes damping times of r-modes in various star models, and finds viscosity regularizes the continuous spectrum and affects gravitational wave damping.

Contribution

It introduces a consistent relativistic framework for shear viscosity in stellar perturbations and provides numerical results on damping times for different star models.

Findings

Viscosity regularizes the continuous spectrum.

Damping times for constant density and polytropic stars agree with estimates within a factor of two.

Realistic neutron star damping times are about 60% larger than previous estimates.

Abstract

We derive the relativistic equations for stellar perturbations, including in a consistent way shear viscosity in the stress-energy tensor, and we numerically integrate our equations in the case of large viscosity. We consider the slow rotation approximation, and we neglect the coupling between polar and axial perturbations. In our approach, the frequency and damping time of the emitted gravitational radiation are directly obtained. We find that, approaching the inviscid limit from the finite viscosity case, the continuous spectrum is regularized. Constant density stars, polytropic stars, and stars with realistic equations of state are considered. In the case of constant density stars and polytropic stars, our results for the viscous damping times agree, within a factor two, with the usual estimates obtained by using the eigenfunctions of the inviscid limit. For realistic neutron stars, our numerical results give viscous damping times with the same dependence on mass and radius as previously estimated, but systematically larger of about 60%.