Generalized optimal statistic for characterizing multiple correlated signals in pulsar timing arrays
Shashwat C. Sardesai, Sarah J. Vigeland, Kyle A. Gersbach, Stephen R. Taylor
Abstract
Pulsar timing arrays are sensitive to low-frequency gravitational waves (GWs), including the low-frequency stochastic gravitational wave background (GWB), which induces correlated changes in millisecond pulsars' timing residuals described by the Hellings-Downs curve. Some sources of noise can also induce correlated changes in pulsar timing residuals, albeit with different correlation signatures. A spatial correlation that differs from Hellings-Downs could also be indicative of non-Einsteinian GW polarizations. It is therefore crucial that we be able to characterize the spatial correlation in order to distinguish between the GWB and sources of noise. The optimal statistic (OS) is a frequentist estimator for the amplitude and significance of a spatially correlated signal in PTA data, and it is widely used to search for the GWB. However, the OS cannot perfectly distinguish between different spatial correlations. In this paper, we introduce the multiple component optimal statistic (MCOS): a generalization of the OS that allows for multiple correlations to be simultaneously fit to the data. We use simulated data to show that this method more accurately recovers injected spatially correlated signals, and in particular eliminates the problem of overestimating the amplitude of correlations that are not present in the data. We also demonstrate that this method can be used to recover multiple correlated signals.