Viscous damping of r-modes: Small amplitude instability

TL;DR

This paper investigates how viscous damping influences the stability of r-modes in compact stars, providing general formulas and analyzing different star types to understand the gravitational wave emission boundaries.

Contribution

It offers general semi-analytic expressions for the instability boundary of r-modes, showing insensitivity to microscopic matter details and applying them to various star models.

Findings

Hybrid stars with small cores can mimic neutron star instability regions.

Neutron stars with high core density exhibit a distinct notch in the instability boundary.

The instability boundary minima are surprisingly insensitive to microscopic matter properties.

Abstract

We study the viscous damping of r-modes of compact stars and analyze in detail the regions where small amplitude modes are unstable to the emission of gravitational radiation. We present general expressions for the viscous damping times for arbitrary forms of interacting dense matter and derive general semi-analytic results for the boundary of the instability region. These results show that many aspects, like in particular the physically important minima of the instability boundary, are surprisingly insensitive to detailed microscopic properties of the considered form of matter. Our general expressions are applied to the cases of hadronic stars, strange stars, and hybrid stars, and we focus on equations of state that are compatible with the recent measurement of a heavy compact star. We find that hybrid stars with a sufficiently small core can "masquerade" as neutron stars and feature an instability region that is indistinguishable from that of a neutron star, whereas neutron stars with a core density high enough to allow direct Urca reactions feature a notch on the right side of the instability region.