Efficient pulsar distance measurement with multiple nanohertz gravitational-wave sources

Abstract: In recent years, pulsar timing arrays (PTAs) have reported evidence for a nanohertz gravitational-wave (GW) background. As radio telescope sensitivity improves, PTAs are also expected to detect continuous gravitational waves from individual supermassive black hole binaries. Nanohertz GWs generate both Earth and pulsar terms in the timing data, and the time delay between the two terms encodes the pulsar distance. Precise pulsar distance measurements are critical to fully exploiting pulsar-term information, which can improve the measurement precision of GW sources' sky position parameters and thus enhance the GW sky-localization capability. In this work, we propose a new pulsar distance estimation method by using pulsar-term phase information from GWs. We construct two-dimensional distance posteriors for pulsar pairs based on the simulated GW signals and combine them to constrain individual pulsar distances. Compared with the existing one-dimensional method, our approach reduces the impact of source-parameter uncertainties on pulsar distance measurements. Considering four GW sources and a PTA of 20 pulsars with a white-noise level of 20 ns, we find that a significant fraction of pulsars at distances $\lesssim 1.4$ kpc can achieve sub-parsec distance precision over a 15-year observation.