Non-Gaussian Statistics of Nanohertz Stochastic Gravitational Waves

TL;DR

This paper develops a semi-analytical framework to characterize the non-Gaussian statistics of nanohertz stochastic gravitational wave backgrounds from supermassive black hole binaries, aiding in distinguishing their origin from early universe processes.

Contribution

It introduces a novel semi-analytical method to calculate non-Gaussian statistics of SGWB from SMBHBs, considering wave interference and source fluctuation effects.

Findings

Non-Gaussian features can help differentiate SMBHBs from early universe sources.

Current and future PTA data can utilize non-Gaussian statistics for source identification.

An approximation of non-Gaussian statistics improves practical Bayesian analysis in PTA data.

Abstract

Recent detection of nHz stochastic gravitational wave background (SGWB) by multiple pulsar timing arrays (PTAs) has stimulated intensive discussions about its physical origin. In principle, either supermassive black hole binaries (SMBHBs) or processes in the early universe may be the sources. 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. In this work, we present a semi-analytical 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.