Orateur
Description
Pulsar Timing Arrays have recently reported strong evidence for a stochastic gravitational wave background. In standard analyses, this is modeled through pulsar-dependent Fourier coefficients assumed to follow Gaussian statistics, so that the signal is fully characterized by its two-point function. However, if the background arises from a finite population of inspiralling supermassive black hole binaries, non-Gaussian features may emerge, making higher-order correlators essential. In this work, we compute the complete four-point correlator of the Fourier coefficients for four arbitrary pulsar positions, identifying it as the leading probe of non-Gaussianity. The result separates into a Gaussian contribution, proportional to the square of the two-point function, and a genuinely non-Gaussian connected component whose angular dependence generalizes the Hellings–Downs correlation to four pulsars. This angular structure depends only on averages of products of antenna pattern functions, and is therefore independent of the specific physical origin of the background. We further propose incorporating the four-point correlator into the parameter-estimation pipeline via a marginalized likelihood that perturbatively accounts for non-Gaussian effects. Our results provide the theoretical framework needed to search for non-Gaussian features in Pulsar Timing Array data, opening the way to a more complete characterization of gravitational-wave backgrounds.