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Reaching diffraction-limited localization with coherent PTAs

Anna C. Tsai1,2,3,*, Dylan L. Jow4,†, and Ue-Li Pen5,1,2,3,6,7

  • *Contact author: anna.tsai@mail.utoronto.ca
  • †Contact author: dylanjow@stanford.edu
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Phys. Rev. D 114, 022003 – Published 9 July, 2026

DOI: https://doi.org/10.1103/q9pv-lrpq

Abstract

Current pulsar timing array (PTA) analyses are phase incoherent and thus to 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 [D. L. Jow et al., How many pixels are there in a polarized pulsar timing array map?, Phys. Rev. D 113, 043034 (2026)]. We present a coherent map-making technique that utilizes precise pulsar distance measurements to reach a diffraction-limited resolution of an individual source: δθdiff×(1/SNR)≈1  arcmin, where δθdiff=λGW/r is the diffractive angle and SNR refers to the detection strength of the source. With this level of angular resolution, identifying an electromagnetic counterpart may become feasible, enabling multimessenger follow-up. We show that for SNR = 10, which may be the current sensitivity level using a coherent analysis, the diffraction limit is reached with approximately ten equidistant pulsars with distances of about 300 parsecs. Moreover, angular resolution scales sharply with the number of known pulsar distances as ∼(1/SNR)Ndist/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.

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Phys. Rev. D 114, 022003– Published 9 July, 2026
  • Received 12 December 2025
  • Accepted 3 June 2026
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