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

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 Ω_gw ∼ 10^-9 for the l = m = 2f-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 ? 9.8. The background from supramassive neutron stars formed from binary mergers peaks at Ω_gw ∼ 10^-10 and should not be detectable, even with third generation interferometers (e.g. Einstein Telescope).