A Numerical Study of Normal Modes of Rotating Neutron Star Models by the Cowling Approximation

Abstract

A numerical method of mode analysis of rapidly rotating relativistic stellar models by the Cowling approximation is applied to rotating neutron stars with realistic equations of state. For selected equations of state, eigenvalues and eigenfunctions of f-modes are numerically solved for stellar models from non-rotating to maximally rotating states. Neutral points of the lower order f-modes are determined as a function of the stellar rotational frequency. As in the polytropic case, we find that the bar mode can have neutral points for models with relatively strong gravity. The rotational frequency at the neutral point increases as the gravitational mass of the model becomes larger. As astrophysical applications of our analysis, we discuss the time scales of gravitational radiation induced instability and the possibility of the resonant excitation of f-modes during inspiraling motion of compact binary systems.

13 pages, 19 figures; 5 new figures are supplemented and some are re-drawn. Accepted for publication in ApJ

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• Nonlinear Pulsations in Differentially Rotating Neutron Stars: Mass-Shedding-Induced Damping and Splitting of the Fundamental Mode
• Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation
• Dynamical Bar Instability in Rotating Stars: Effect of General Relativity
• The f-mode instability in relativistic neutron stars
• Frequencies of f-modes in differentially rotating relativistic stars and secular stability limits
• Quasi-radial modes of rotating stars in general relativity
• General-relativistic treatment of tidal $g$-mode resonances in coalescing binaries of neutron stars. I. Theoretical framework and crust breaking
• Excitation of f-modes during mergers of spinning binary neutron star
• Dynamics of Fast Rotating Neutron Stars: An Approach in the Hilbert Gauge
• A new approach to the study of quasi-normal modes of rotating stars
• Fast Rotating Neutron Stars: Oscillations and Instabilities
• Eigenmode frequency distribution of rapidly rotating neutron stars
• Oscillations of Highly Magnetized Non-rotating Neutron Stars
• A characteristic approach to the quasi-normal mode problem
• Non-axisymmetric oscillations of rapidly rotating relativistic stars by conformal flatness approximation
• Gravitational Waves from Rotating Proto-Neutron Stars
• Neutron star evolution with the Bemfica-Disconzi-Noronha-Kovtun viscous hydrodynamics framework
• Importance of Perturbed Gravitational Potentials in Differentially Rotating Newtonian Stars
• Fundamental modes of rotating neutron stars with various degrees of differential rotation in dynamical spacetimes