Up the Amps: Determining threshold for Pairwise Covariance in PTAs

Evidence for a gravitational wave background (GWB) has been steadily accumulating with supporting evidence from pulsar timing array collaborations across the globe. A crucial step in these analyses is GWB parameter estimation and significance testing, both of which can be done using the frequentist PTA optimal statistic (OS). The OS has been used extensively for many years, however, recent works have shown that the assumptions used to construct the OS are beginning to break down. In response, a more robust method that includes correlations between pulsar pairs called pair covariance (PC) has been developed. The inclusion of PC has been shown to fix the bias in the OS in recent datasets, though at the cost of a 4 order of magnitude increase in computational runtime. The focus of this poster is to determine a threshold for PC. Determining such a threshold can prove tremendously useful in determining if new data sets require PC and if any older analyses need to be redone. We find a clear relationship between the signal-to-noise ratio (SNR) and the ratio in measured uncertainties between the OS and PC for various PTA configurations. This allows us to set thresholds for any given PTA configuration parameter while also enabling estimates of the more costly PC before fully calculating it.