Inertial modes of slowly rotating relativistic stars in the Cowling approximation

Abstract

We study oscillations of slowly rotating relativistic barotropic as well as non-barotropic polytropic stars in the Cowling approximation, including first order rotational corrections. By taking into account the coupling between the polar and axial equations, we find that, in contrast to previous results, the $m=2$ $r$ modes are essentially unaffected by the continuous spectrum and exist even for very relativistic stellar models. We perform our calculations both in the time and frequency domain. In order to numerically solve the infinite system of coupled equations, we truncate it at some value $l_{\max }$. Although the time dependent equations can be numerically evolved without any problems, the eigenvalue equations possess a singular structure, which is related to the existence of a continuous spectrum. This prevents the numerical computation of an eigenmode if its eigenfrequency falls inside the continuous spectrum. The properties of the latter depend strongly on the cut-off value $l_{\max }$ and it can consist of several either disconnected or overlapping patches, which are the broader the more relativistic the stellar model is. By discussing the dependence of the continuous spectrum as a function of both the cut-off value $l_{\max }$ and the compactness $M/R$, we demonstrate how it affects the inertial modes. Through the time evolutions we are able to show that some of the inertial modes can actually exist inside the continuous spectrum, but some cannot. For more compact and therefore more relativistic stellar models, the width of the continuous spectrum strongly increases and as a consequence, some of the inertial modes, which exist in less relativistic stars, disappear.

18 pages, 4 figures, MNRAS typesetting

References in corpus (17)

• The r-mode instability in rotating neutron stars
• R-Mode Oscillations in Rotating Magnetic Neutron Stars
• Where are the r-modes of isentropic stars?
• The rotational modes of relativistic stars: Analytic results
• Nonlinear r-modes in Rapidly Rotating Relativistic Stars
• Axisymmetric Modes of Rotating Relativistic Stars in the Cowling Approximation
• Generalized r-Modes of the Maclaurin Spheroids
• On the r-mode spectrum of relativistic stars
• Rotational modes of non-isentropic stars and the gravitational radiation driven instability
• Inertial modes of slowly rotating isentropic stars
• On the r-mode spectrum of relativistic stars in the low-frequency approximation
• On the r-mode spectrum of relativistic stars: Inclusion of the radiation reaction
• Relativistic r-modes in Slowly Rotating Neutron Stars: Numerical Analysis in the Cowling Approximation
• Evolution equations for the perturbations of slowly rotating relativistic stars
• r-modes of slowly rotating non-isentropic relativistic stars
• Approximate equation relevant to axial oscillations on slowly rotating relativistic stars
• R-mode Instability of Slowly Rotating Non-isentropic Relativistic Stars

Cited by in corpus (24)

• Rotating Stars in Relativity
• Rotating Stars in Relativity
• Isolated and Binary Neutron Stars in Dynamical Chern-Simons Gravity
• The rotational modes of relativistic stars: Numerical results
• Relativistic g-modes in rapidly rotating neutron stars
• Oscillations of rapidly rotating relativistic stars
• Black hole scalarization induced by the spin -- 2+1 time evolution
• The electromagnetic signature of black hole ringdown
• R-mode oscillations of rapidly rotating barotropic stars in general relativity: Analysis by the relativistic Cowling approximation
• Rotational effects on the oscillation frequencies of newly born proto-neutron stars
• Regularizing the r-mode problem for nonbarotropic relativistic stars
• Inertial modes of rigidly rotating neutron stars in Cowling approximation
• Non-axisymmetric oscillations of differentially rotating relativistic stars
• R-mode frequencies of rapidly and differentially rotating relativistic neutron stars
• Eigenmode frequency distribution of rapidly rotating neutron stars
• Evolution equations for slowly rotating stars
• The effect of magnetic fields on the r-modes of slowly rotating relativistic neutron stars
• The r-modes of slowly rotating, stratified neutron stars
• Slowly rotating neutron stars with small differential rotation: equilibrium models and oscillations in the Cowling approximation
• Nonlinear Decay of r modes in Rapidly Rotating Neutron Stars
• Gravitational Waves from Rotating Proto-Neutron Stars
• Toroidal oscillations of slowly rotating relativistic star in tensor-vector-scalar theory
• Formulating the r-mode problem for slowly rotating neutron stars
• Impact of the relativistic Cowling approximation on shear and interface modes of neutron stars