The Effect of Orbital Eccentricity on Gravitational Wave Background Radiation from Cosmological Binaries

A compact binary on an eccentric orbit radiates gravitational waves (GWs) at all integer harmonics of its orbital frequency. Thus, the spectral energy distribution, the power and the timescale of GW radiation of a binary on an eccentric orbit are different from those of a binary on a circular orbit. Therefore, in order to predict spectra of gravitational wave background radiation (GWBR) from compact binaries, it is important to include the effect of orbital eccentricity of binaries. In this study, we investigate the effect of orbital eccentricity on expected GWBR from extragalactic compact binaries. For this purpose, we formulate the power spectrum of GWBR from cosmological evolving eccentric binaries. Then we apply this formulation to the case of the GWBR from supermassive black hole (SMBH) binaries in galaxy nuclei. The key to do this is correctly estimating the number density of coalescing SMBH binaries. In this study, we use a semi-analytic model of galaxy and SMBH formation. We find that the power spectrum of the GWBR from SMBH binaires on eccentric orbits is suppressed for frequencies . 1nHz dependent on an assumed initial eccentricity. Our model predicts that while the overall shape and amplitude of the power spectrum depend largely on galaxy formation processes, eccentricity of binaries can affect the shape of the power spectrum for lower frequencies . 1nHz. Pulsar timing measurements, which can detect GW at this frequency range, would be able to constrain the effect of eccentricity on the power spectrum of the GWBR from SMBH binaries.