Inertial modes in slowly rotating stars : an evolutionary description

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.

36 pages, 27 figures, accepted for publication in Phys. Rev. D (discussion added in the introduction)

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• Nonlinear r-modes in neutron stars: A hydrodynamical limitation on r-mode amplitudes
• Inertial modes of non-stratified superfluid neutron stars
• A new approach to the study of quasi-normal modes of rotating stars
• Relativistic r-modes and Shear viscosity: regularizing the continuous spectrum
• MHD of rotating compact stars with spectral methods: description of the algorithm and tests
• Summation by parts methods for the spherical harmonic decomposition of the wave equation in arbitrary dimensions
• Numerical simulations of oscillating and differentially rotating neutron stars
• Inertial modes in stratified rotating neutron stars : An evolutionary description