Saturation of the f-mode instability in neutron stars: I. Theoretical framework

TL;DR

This paper develops a theoretical framework for understanding how nonlinear mode coupling can saturate the f-mode instability in rotating neutron stars, affecting gravitational wave emission predictions.

Contribution

It introduces a detailed model of quadratic mode coupling and three-mode networks, providing insights into the nonlinear saturation mechanism of the f-mode instability.

Findings

Quadratic mode coupling can lead to saturation of the f-mode instability.

Three-mode networks exchange energy, influencing mode amplitudes.

Saturation amplitude impacts gravitational wave signals from neutron stars.

Abstract

The basic formulation describing quadratic mode coupling in rotating Newtonian stars is presented, focusing on polar modes. Due to the Chandrasekhar-Friedman-Schutz mechanism, the f-mode (fundamental oscillation) is driven unstable by the emission of gravitational waves. If the star falls inside the so-called instability window, the mode's amplitude grows exponentially, until it is halted by nonlinear effects. Quadratic perturbations form three-mode networks inside the star, which evolve as coupled oscillators, exchanging energy. Coupling of the unstable f-mode to other (stable) modes can lead to a parametric resonance and the subsequent saturation of its amplitude, thus suppressing the instability. The saturation point determines the amplitude of the gravitational-wave signal obtained from an individual source, as well as the evolutionary path of the latter inside the instability window.