On the r-mode spectrum of relativistic stars: Inclusion of the radiation reaction

TL;DR

This paper investigates the r-mode oscillations in relativistic neutron stars, revealing that relativistic effects can suppress or eliminate the instability predicted by Newtonian theory, especially in more compact models.

Contribution

It provides a detailed analysis of relativistic corrections to r-modes using slow-rotation formalism across various stellar models, highlighting the impact on instability growth.

Findings

Relativistic models show weakened or absent r-mode instability compared to Newtonian predictions.

In certain polytropic models, r-modes disappear and decay instead of growing.

Relativistic effects are significant in more compact neutron star models, altering the expected gravitational wave emission.

Abstract

We consider both mode calculations and time evolutions of axial r-modes for relativistic uniformly rotating non-barotropic neutron stars, using the slow-rotation formalism, in which rotational corrections are considered up to linear order in the angular velocity \Omega. We study various stellar models, such as uniform density models, polytropic models with different polytropic indices n, and some models based on realistic equations of state. For weakly relativistic uniform density models, and polytropes with small values of n, we can recover the growth times predicted from Newtonian theory when standard multipole formulae for the gravitational radiation are used. However, for more compact models, we find that relativistic linear perturbation theory predicts a weakening of the instability compared to the Newtonian results. When turning to polytropic equations of state, we find that for certain ranges of the polytropic index n, the r-mode disappears, and instead of a growth, the time evolutions show a rapid decay of the amplitude. This is clearly at variance with the Newtonian predictions. It is, however, fully consistent with our previous results obtained in the low-frequency approximation.