Saturation of the f-mode instability in neutron stars: II. Applications and results

TL;DR

This paper investigates how nonlinear mode coupling causes the saturation of the f-mode instability in neutron stars, affecting gravitational wave signals and providing insights into the star's internal physics.

Contribution

It presents the first detailed analysis of nonlinear mode coupling leading to f-mode saturation in neutron stars, with applications to different astrophysical scenarios.

Findings

Saturation amplitudes vary significantly during star evolution.

Multiple daughter mode pairs can couple to the parent mode.

Results depend on the star's evolutionary stage and initial conditions.

Abstract

We present the first results on the saturation of the f-mode instability in neutron stars, due to nonlinear mode coupling. Emission of gravitational waves drives the f-mode (fundamental mode) unstable in fast-rotating, newborn neutron stars. The initial growth phase of the mode is followed by its saturation, because of energy leaking to other modes of the star. The saturation point determines the strain of the generated gravitational-wave signal, which can then be used to extract information about the neutron star equation of state. The parent (unstable) mode couples via parametric resonances with pairs of daughter modes, with the triplets' evolution exhibiting a rich variety of behaviors. We study both supernova- and merger-derived neutron stars, simply modeled as polytropes in a Newtonian context, and show that the parent may couple to many different daughter pairs during the star's evolution through the instability window, with the saturation amplitude changing by orders of magnitude.