Modeling nonstationary noise in pulsar timing array data analysis

Pulsar timing array (PTA) collaborations recently reported evidence for the presence of a gravitational wave background (GWB) in their datasets. The main candidate that is expected to produce such a GWB is the population of supermassive black hole binaries. Some analyses showed that the recovered signal may exhibit time-dependent properties, i.e., nonstationarity. In this paper, we propose an approximated nonstationary Gaussian process model obtained from the perturbation of stationary processes. The presented method is applied to the second data release of the European Pulsar Timing Array to search for nonstationary features in the GWB. We analyzed the data in different time slices and showed that the inferred properties of the GWB evolve with time. We find no evidence for such nonstationary behavior and the Bayes factor in favor of the latter is $B_S^{\mathrm{NS}}=1.5$. We argue that the evolution of the GWB properties most likely comes from the improvement of the observation cadence with time and better characterization of the noise of individual pulsars. Such nonstationary GWB could also be produced by the leakage of nonstationary features in the noise of individual pulsars or by the presence of an eccentric single source.