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

A compact binary in an eccentric orbit radiates gravitational waves (GWs) atall integer harmonics of its orbital frequency. In this study, we investigatethe effect of orbital eccentricity on the expected gravitational backgroundradiation (GWBR) from supermassive black hole (SMBH) binaries in the nuclei ofgalaxies. For this purpose, we formulate a power spectrum of the GWBR fromcosmological evolving eccentric binaries. Then, we apply this formulation tothe case of the GWBR from SMBH binaries. The key to doing this is to correctlyestimate the number density of coalescing SMBH binaries. In this study, we usea semi-analytic model of galaxy and SMBH formation. We find that the powerspectrum of the GWBR from SMBH binaries on eccentric orbits is suppressed forfrequencies $f \lesssim 1~{\rm nHz}$ if the initial eccentricity, $e_0$,satisfies $e_0 > 0.2$ and the initial semi-major axis is 300 times Scwarzschildradius. Our model predicts that while the overall shape and amplitude of thepower spectrum depend strongly on the processes of galaxy formation, theeccentricity of binaries can affect the shape of the power spectrum for lowerfrequencies, i.e., $f \lesssim 1~{\rm nHz}$. Pulsar timing measurements, whichcan detect GW in this frequency range, could constrain the effect ofeccentricity on the power spectrum of the GWBR from SMBH binaries.Comment: 16 pages, 12 figures, typos correced, matched to the published versio