Frequencies of f-modes in differentially rotating relativistic stars and secular stability limits

TL;DR

This study calculates f-mode eigenfrequencies in differentially rotating relativistic stars using the Cowling approximation, revealing how differential rotation influences secular stability limits and the onset of gravitational radiation-driven instabilities.

Contribution

It provides the first detailed analysis of f-mode frequencies in differentially rotating relativistic stars and their impact on secular stability thresholds.

Findings

Secular instability onset occurs at higher beta in differentially rotating stars.

Differential rotation extends the maximum beta for equilibrium models.

Differential rotation generally favors earlier onset of f-mode instabilities.

Abstract

We have computed the eigenfrequencies of f-modes for a constant-rest-mass sequences of rapidly rotating relativistic inviscid stars in differential rotation. The frequencies have been calculated neglecting the metric perturbations (the relativistic Cowling approximation) and expressed as a function of the ratio between the rotational kinetic energy and the absolute value of the gravitational energy of the stellar model beta=T/|W|. The zeros and the end-points of these sequences mark respectively the onset of the secular instability driven by gravitational radiation-reaction and the maximum value of beta at which an equilibrium model exists. In differentially rotating stars the secular stability limits appear at a beta larger than those found for uniformly rotating stars. Differential rotation, on the other hand, also allows for the existence of equilibrium models at values of beta larger than those for uniformly rotating stars, moving the end-point of the sequences to larger beta. As a result, for some degrees of differential rotation, the onset of the secular instability for f-modes is generally favoured by the presence of differential rotation.