r-modes of slowly rotating non-isentropic relativistic stars

TL;DR

This paper studies r-modes in slowly rotating relativistic stars, finding that discrete solutions exist only for certain polytropic models and are absent in typical neutron star models with higher relativistic factors.

Contribution

It demonstrates the conditions under which discrete r-mode solutions exist in relativistic stars, highlighting limitations for models with higher relativistic factors.

Findings

Discrete r-mode solutions exist only for specific polytropic indices.

No discrete solutions for the l=m=2 r-mode in models with N > 1.18.

For N=1 polytropes, solutions are absent when M/R > 0.1.

Abstract

We investigate properties of r-modes characterized by regular eigenvalue problem in slowly rotating relativistic polytropes. Our numerical results suggest that discrete r-mode solutions for the regular eigenvalue problem exist only for restricted polytropic models. In particular the r-mode associated with l=m=2, which is considered to be the most important for gravitational radiation driven instability, do not have a discrete mode as solutions of the regular eigenvalue problem for polytropes having the polytropic index N > 1.18 even in the post-Newtonian order. Furthermore for a N=1 polytrope, which is employed as a typical neutron star model, discrete r-mode solutions for regular eigenvalue problem do not exist for stars whose relativistic factor M/R is larger than about 0.1. Here M and R are stellar mass and stellar radius, respectively.