Formulating the r-mode problem for slowly rotating neutron stars

TL;DR

This paper reevaluates the r-mode problem in stratified neutron stars, proposing new computational strategies to better understand their oscillations and implications for gravitational-wave detection.

Contribution

It introduces revised methods for analyzing r-modes in non-barotropic neutron stars, addressing previous issues with singularities and computational approaches.

Findings

Traditional approaches face issues with singularities at co-rotation points.

Numerical methods are necessary for moderate to slow rotators.

Slow-rotation approximations are feasible for the fastest spinning stars.

Abstract

We revisit the problem of inertial r-modes in stratified stars, drawing on a more precise description of the composition stratification in a mature neutron star. The results highlight issues with the traditional approach to the problem, leading us to rethink the computational strategy for r-modes of non-barotropic neutron stars. We outline two strategies for dealing with the problem. For moderate to slowly rotating neutron stars the only viable alternative may be to approach the problem numerically from the outset, while a meaningful slow-rotation calculation can be carried out for the fastest known spinning stars (which may be close to being driven unstable by the emission of gravitational waves). We demonstrate that the latter approach leads to a problem close, but not identical, to that for barotropic inertial modes. We also suggest that these reformulations of the problem likely resolve the long-standing problem of singular behaviour associated with a co-rotation point in rotating relativistic neutron stars. This issue needs to be resolved in order to guide future gravitational-wave searches.