Stochastic Background of Gravitational Waves Generated by Eccentric Neutron Star Binaries

TL;DR

This paper models the stochastic gravitational wave background from eccentric neutron star binaries, analyzing harmonic contributions and eccentricity effects, and discusses detection prospects with space-based detectors and pulsar timing arrays.

Contribution

It introduces a harmonic-summation method for calculating the gravitational wave background from eccentric binaries and explores the impact of eccentricity distributions.

Findings

Harmonics significantly influence the gravitational wave spectrum.

Eccentricity distribution affects the amplitude and shape of the background.

Detection prospects vary with different eccentricity models.

Abstract

Binary systems emit gravitational waves in a well-known pattern; for binaries in circular orbits, the emitted radiation has a frequency that is twice the orbital frequency. Systems in eccentric orbits, however, emit gravitational radiation in the higher harmonics too. In this paper, we are concerned with the stochastic background of gravitational waves generated by double neutron star systems of cosmological origin in eccentric orbits. We consider in particular the long-lived systems, that is, those binaries for which the time to coalescence is longer than the Hubble time ($\sim 10$Gyr). Thus, we consider double neutron stars with orbital frequencies ranging from $10^{-8}$ to $2\times 10^{-6}$Hz. Although in the literature some papers consider the spectra generated by eccentric binaries, there is still space for alternative approaches for the calculation of the backgrounds. In this paper, we use a method that consists in summing the spectra that would be generated by each harmonic separately in order to obtain the total background. This method allows us to clearly obtain the influence of each harmonic on the spectra. In addition, we consider different distribution functions for the eccentricities in order to investigate their effects on the background of gravitational waves generated. At last, we briefly discuss the detectability of this background by space-based gravitational wave antennas and pulsar timing arrays.