An Accurate Modeling of Nano-hertz Gravitational Wave Signal from Eccentric Supermassive Binary Black Holes: An Essential Step Toward a Robust Discovery

Abstract The stochastic gravitational wave background (SGWB) in the nanohertz (nHz) regime, detectable by pulsar timing arrays (PTAs), provides a promising probe of the cosmic population of supermassive black hole binaries (SMBHBs). These binaries are expected to retain significant eccentricity throughout their evolution. We present a new technique to model the nHz SGWB by incorporating eccentricity into a multiscale adaptive simulation framework. Using the time-domain eccentric waveform model ESIGMAHM , we generate realistic GW signals from astrophysical populations of SMBHBs. Unlike circular binaries, eccentric systems emit across multiple frequencies, introducing spectral correlations between frequency bins. These correlations provide a novel observational signature of the eccentricity distribution of the SMBHB population. In this work, we adopt simplified power-law models for the eccentricity distribution. While this does not capture the full complexity of galactic environments, it effectively highlights the key features of GW emission from eccentric binaries and their imprint on the SGWB. Our approach advances nHz GW signal modeling by incorporating eccentricity at small scales, enabling more realistic predictions and offering a new avenue for probing SMBHB astrophysics with future PTA observations.