Supermassive Black Hole Gravitational Wave Background Exhibits Non-Gaussianity

This paper investigates the non-Gaussian features of the gravitational wave (GW) background generated by a population of inspiraling supermassive black hole (SMBH) binaries. The authors demonstrate that the SMBH GW amplitude distribution (GWAD) exhibits a universal heavy power-law tail proportional to A⁻⁴, while the low-amplitude tail depends on the SMBH merger rate and the energy-loss mechanisms of the binaries. The distribution of the induced timing residuals inherits this heavy tail, leading to the divergence of ensemble averaged statistical moments of order three and higher. This limits their usefulness as measures of non-Gaussianity and indicates that the GW background from SMBH binaries exhibits the single loud source principle. The authors confirm that the variance-averaged Gaussian approximation accurately describes the timing residual statistics and justify a factored likelihood structure that combines standard Gaussian-process PTA posteriors with the non-Gaussian population prior. They provide a fast and flexible Python implementation to compute the distribution of timing residuals from a given SMBH merger rate or GWAD. This research has significant implications for the accurate modeling and inference of SMBH merger rates and the detection of individual sources within the GW background.

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