Eccentricity effects on the supermassive black hole gravitational wave background

Abstract: We studied how eccentricity affects the gravitational wave (GW) spectrum from supermassive black hole (SMBH) binaries. We developed a fast and accurate semi-analytic method for computing the GW spectra, the distribution for the spectral fluctuations and the correlations between different frequencies. As GW emission circularizes binaries, the suppression of the signal strength due to eccentricity is relevant for signals from wider binaries emitting at lower frequencies. Such a feature is present in the signal observed at pulsar timing arrays. We found that when orbital decay of the SMBH binaries is driven by GWs only, the shape of the observed signal preferred highly eccentric binaries $\langle e \rangle_{2\,{\rm nHz}} = 0.83^{+0.04}_{-0.05}$. However, when environmental effects were included, the initial eccentricity could be significantly lowered, yet the scenario with purely circular binaries was still mildly disfavored.