Two-Dimensional Pulsar Distance Inference from Nanohertz Gravitational Waves

Pulsar timing arrays (PTAs) are limited in localizing nanohertz continuous gravitational waves (CGWs) by uncertainties in pulsar distances. We introduce a method to infer pulsar distances in two dimensions, using phase information from the pulsar terms of multiple CGW sources. Our approach can enhance distance precision and, in some cases, achieve order-of-magnitude improvements relative to existing one-dimensional distance-inference methods. Using simulations of an SKA-era PTA with realistic parallax-based distance priors, we demonstrate that pulsars at $\sim 1$ kpc can achieve sub-parsec distance precision with only a few CGW sources. Such improvements in pulsar-distance precision have important implications for CGW host-galaxy identification and multimessenger observational prospects.