Reaching diffraction-limited localization with coherent PTAs

TL;DR

This paper demonstrates that incorporating precise pulsar distance measurements into PTA analyses can achieve diffraction-limited localization of gravitational-wave sources, significantly enhancing angular resolution and detection sensitivity.

Contribution

It introduces a coherent map-making technique that utilizes pulsar distances to reach diffraction-limited resolution, enabling potential multi-messenger follow-up of GW sources.

Findings

Diffraction-limited resolution of ~2 arcmin is achievable with SNR=10 and about 9 pulsars.

Angular resolution improves sharply with additional pulsar distance measurements, scaling as (1/SNR)^{N_dist/2}.

Current pulsar distance constraints are already at sub-parsec levels, supporting the feasibility of this approach.

Abstract

Current pulsar timing array (PTA) analyses do not take full advantage of pulsar distance information, thereby missing out on improved angular resolution and on a potential factor-of-two gain in detection sensitivity for individual gravitational-wave (GW) sources. In this work, we investigate the impact of precise pulsar distance measurements on angular resolution as an extension to previous work measuring the angular resolution of a dense, isotropic PTA [Jow et al., 2025]. We present a coherent map-making technique that utilizes precise pulsar distance measurements to reach the diffraction-limited resolution of an individual source: $\delta \theta_{\mathrm{diff}} \sim (1/\mathrm{SNR})(\lambda_{\mathrm{GW}}/r) \approx 2~\mathrm{arcmin}$, where the SNR refers to the detection strength of the source. With this level of angular resolution, identifying an EM counterpart may become feasible, enabling multi-messenger follow-up. We show that for $\rm SNR=10$, which may be the current sensitivity level using a coherent analysis, the diffraction limit is reached with roughly 9 pulsars. Moreover, angular resolution scales sharply with the number of known pulsar distances as $\sim (1/\mathrm{SNR})^{N_{\mathrm{dist}}/2}$. Thus, each additional pulsar with high signal-to-noise timing and precise distance measurement can improve PTA resolution by an order of magnitude. The distance to the best-timed millisecond pulsar (PSR J0437$-$4715) is already constrained to sub-parsec levels. We argue, therefore, that a coherent analysis of PTA data, fully incorporating pulsar distance information, is timely.