The Effect of Orbital Eccentricity on Gravitational Wave Background Radiation from Supermassive Black Hole Binaries

A compact binary on an eccentric orbit radiates gravitational waves (GWs) at all integer harmonics of its orbital frequency. In this study, we investigate the effect of orbital eccentricity on expected gravitational background radiation (GWBR) from supermassive black hole (SMBH) binaries in galaxy nuclei. 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 SMBH binaries. 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 binaries on eccentric orbits is suppressed for frequencies . 1nHz if the initial eccentricity is e0 > 0.2 and the initial semi-major axis is 300 times Scwarzschild radius. 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.