Non-Gaussian statistics of nanohertz stochastic gravitational waves

Multiple pulsar timing arrays (PTAs) have recently reported evidence for nHz stochastic gravitational wave background (SGWB), stimulating intensive discussions about its physical origin. In principle, the sources may be either supermassive black hole binaries (SMBHBs) or processes in the early Universe. One key difference between the two lies in the statistics of the SGWB frequency power spectrum. In particular, the often assumed Gaussian random SGWB does not accurately describe the distribution of the collective SMBHB emission. This work presents a semianalytical framework for calculating the non-Gaussian statistics of SGWB power expected from SMBHBs. We find that (a) wave interference between individual SMBHBs with indistinguishable observed frequencies and (b) the Poisson fluctuation of the source numbers, together shape the non-Gaussian statistics. Implementing the non-Gaussian statistics developed in this work, we investigate the sensitivity of current and future PTA datasets in distinguishing the origin of the SGWB through non-Gaussian information. Additionally, we find an interesting approximation of the non-Gaussian statistics, which has implications for accurately and practically treating non-Gaussianity in PTA Bayesian analyses. Published by the American Physical Society 2025