R-Modes in Superfluid Neutron Stars

TL;DR

This paper investigates r-modes in superfluid neutron stars, deriving equations for higher-order effects, and finds that mutual friction damping generally cannot suppress gravitational wave instabilities, except in specific superfluid models.

Contribution

It provides a detailed numerical analysis of superfluid r-modes, including the effects of mutual friction damping, which was previously not well understood.

Findings

Mutual friction damping time-scale is about 10^4 seconds for typical models.

Most superfluid models cannot suppress gravitational wave instabilities.

A small subset of models can damp instabilities within about 5 seconds.

Abstract

The analogs of r-modes in superfluid neutron stars are studied here. These modes, which are governed primarily by the Coriolis force, are identical to their ordinary-fluid counterparts at the lowest order in the small angular-velocity expansion used here. The equations that determine the next order terms are derived and solved numerically for fairly realistic superfluid neutron-star models. The damping of these modes by superfluid ``mutual friction'' (which vanishes at the lowest order in this expansion) is found to have a characteristic time-scale of about 10^4 s for the m=2 r-mode in a ``typical'' superfluid neutron-star model. This time-scale is far too long to allow mutual friction to suppress the recently discovered gravitational radiation driven instability in the r-modes. However, the strength of the mutual friction damping depends very sensitively on the details of the neutron-star core superfluid. A small fraction of the presently acceptable range of superfluid models have characteristic mutual friction damping times that are short enough (i.e. shorter than about 5 s) to suppress the gravitational radiation driven instability completely.