Inertial modes in slowly rotating stars : an evolutionary description

TL;DR

This paper introduces a spectral method-based hydro code to study inertial modes in slowly rotating neutron stars, using an anelastic approximation to efficiently simulate their evolution and analyze mode behavior.

Contribution

The paper presents a new spectral hydro code employing the anelastic approximation for studying inertial modes in rotating stars, with preliminary linear results and comparisons to existing eigenvector calculations.

Findings

Velocity concentrates near the equator in simulations.

Results align with previous eigenvector studies.

Velocity exhibits a persistent polar component.

Abstract

We present a new hydro code based on spectral methods using spherical coordinates. The first version of this code aims at studying time evolution of inertial modes in slowly rotating neutron stars. In this article, we introduce the anelastic approximation, developed in atmospheric physics, using the mass conservation equation to discard acoustic waves. We describe our algorithms and some tests of the linear version of the code, and also some preliminary linear results. We show, in the Newtonian framework with differentially rotating background, as in the relativistic case with the strong Cowling approximation, that the main part of the velocity quickly concentrates near the equator of the star. Thus, our time evolution approach gives results analogous to those obtained by Karino {\it et al.} \cite{karino01} within a calculation of eigenvectors. Furthermore, in agreement with the work of Lockitch {\it et al.} \cite{lockandf01}, we found that the velocity seems to always get a non-vanishing polar part.