A Nonlinear Coupling Network to Simulate the Development of the r-mode Instablility in Neutron Stars I. Construction

TL;DR

This paper develops an analytical model of nonlinear mode coupling in rotating neutron stars to understand the development of r-mode instability, providing detailed coupling coefficients and damping values.

Contribution

It introduces an analytical method to compute mode coupling coefficients and damping effects in neutron stars, advancing the understanding of r-mode instability saturation.

Findings

Computed all mode couplings up to n=30

Provided analytic shear damping and normalization values

Laid groundwork for numerical simulations of mode interactions

Abstract

R-modes of a rotating neutron star are unstable because of the emission of gravitational radiation. We explore the saturation amplitudes of these modes determined by nonlinear mode-mode coupling. Modelling the star as incompressible allows the analytic computation of the coupling coefficients. All couplings up to n=30 are obtained, and analytic values for the shear damping and mode normalization are presented. In a subsequent paper we perform numerical simulations of a large set of coupled modes.