The stochastic background of gravitational waves due to the f-mode instability in neutron stars

TL;DR

This paper estimates the stochastic gravitational wave background from hot, young neutron stars with f-mode instabilities, predicting detectable signals from supernovae but not from binary mergers.

Contribution

It provides the first detailed spectral estimate of the gravitational wave background from f-mode instabilities in neutron stars, linking formation rates to cosmic star formation.

Findings

Background peaks at $ imes 10^{-9}$ for supernovae-derived neutron stars.

Detection prospects are promising with second-generation interferometers.

Binary merger neutron stars produce a weaker background, unlikely to be detected.

Abstract

This paper presents an estimate for the spectral properties of the stochastic background of gravitational waves emitted by a population of hot, young, rapidly rotating neutron stars throughout the Universe undergoing $f$-mode instabilities, formed through either core-collapse supernova explosions or the merger of binary neutron star systems. Their formation rate, from which the gravitational wave event rate is obtained, is deduced from observation-based determinations of the cosmic star formation rate. The gravitational wave emission occurs during the spin-down phase of the $f$-mode instability. For low magnetized neutron stars and assuming 10\% of supernova events lead to $f$-mode unstable neutron stars, the background from supernova-derived neutron stars peaks at $\Omega_{\text{gw}} \sim 10^{-9}$ for the $l=m=2$ $f$-mode, which should be detectable by cross-correlating a pair of second generation interferometers (e.g. Advanced LIGO/Virgo) with an upper estimate for the signal-to-noise ratio of $\approx$ 9.8. The background from supramassive neutron stars formed from binary mergers peaks at $\Omega_{\text{gw}} \sim 10^{-10}$ and should not be detectable, even with third generation interferometers (e.g. Einstein Telescope).