Optimizing Pulsar Timing Array Observational Cadences for Sensitivity to Low-Frequency Gravitational Wave Sources

We can improve the sensitivity of a pulsar timing array (PTA) to different gravitational-wave sources by observing pulsars with low timing noise over years to decades and distributed across the sky. We discuss observing strategies for a PTA focused on a stochastic gravitational-wave background or single continuous-wave sources. We describe the method to calculate a PTA's sensitivity to different gravitational-wave-source classes. We then apply our method to the 45 pulsars presented in the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 11-year data set. For expected amplitudes of the stochastic background, we find that all pulsars contribute significantly over the timescale of decades; the exception is for very pessimistic values of the background amplitude. For individual single sources, we find that a number of pulsars contribute to the sensitivity of a given source but that which pulsars contribute are different depending on the source, or versus an all-sky metric. Our results show that it is also imperative to locate and time as many high-precision pulsars as possible, as quickly as possible, to maximize the sensitivity of next-generation PTA detectors.