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

Abstract

A compact binary in 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 the expected gravitational background radiation (GWBR) from supermassive black hole (SMBH) binaries in the nuclei of galaxies. For this purpose, we formulate a power spectrum of the GWBR from cosmological evolving eccentric binaries. Then, we apply this formulation to the case of the GWBR from SMBH binaries. The key to doing this is to correctly estimate 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 $f \lesssim 1~{\rm nHz}$ if the initial eccentricity, $e_0$, satisfies $e_0 > 0.2$ 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 strongly on the processes of galaxy formation, the eccentricity of binaries can affect the shape of the power spectrum for lower frequencies, i.e., $f \lesssim 1~{\rm nHz}$. Pulsar timing measurements, which can detect GW in this frequency range, could constrain the effect of eccentricity on the power spectrum of the GWBR from SMBH binaries.