Investigating Bias from Using a Subset of Pulsars as a Pulsar Timing Array*

Pulsar timing arrays (PTAs) aim to detect gravitational waves (GWs) by using millisecond pulsars as extremely stable clocks thereby creating a galaxy-wide GW detector. PTAs are predicted to detect a stochastic gravitational wave background (GWB) from a population of gravitational waves emitted from supermassive black hole binaries. PTA collaborations such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), the Parkes Pulsar Timing Array (PPTA), and the European Pulsar Timing Array (EPTA) have recently found a common-spectrum process in their data. However, the median amplitude values for all three detections are in tension with some of the previously computed upper limits. We investigate how using a subset of a set of pulsars affects computing upper limits in order to help explain why previous upper limits might have been biased toward lower values.