Searching for A Generic Gravitational Wave Background via Bayesian Nonparametric Analysis with Pulsar Timing Arrays

Gravitational wave background results from the superposition of gravitational waves generated from all sources across the Universe. Previous efforts on detecting such a background with pulsar timing arrays assume it is an isotropic Gaussian background with a power law spectrum. However, when the number of sources is limited, the background might be non-Gaussian or the spectrum might not be a power law. Correspondingly previous analysis may not work effectively. Here we use a method --- Bayesian Nonparametric Analysis --- to try to detect a generic gravitational wave background, which directly sets constraints on the feasible shapes of the pulsar timing signals induced by a gravitational wave background and allows more flexible forms of the background. Our Bayesian nonparametric analysis will infer if a gravitational wave background is present in the data, and also estimate the parameters that characterize the background. This method will be much more effective than the conventional one assuming the background spectrum follows a power law in general cases. While the context of our discussion focuses on pulsar timing arrays, the analysis itself is directly applicable to detect and characterize any signals that arise from the superposition of a large number of astrophysical events.