Optimising gravitational-wave sky maps for pulsar timing arrays

¹ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
² School of Physics and Astronomy, Monash University, Clayton VIC 3800, Australia
³ OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery, Clayton VIC 3800, Australia
⁴ Jodrell Bank Centre for Astrophysics, University of Manchester, Department of Physics and Astronomy, Alan-Turing Building, Oxford Street, Manchester M13 9PL, UK
⁵ Department of Physics and Astronomy, Vanderbilt University, 2301 Vanderbilt Place, Nashville, TN 37235, USA
⁶ OzGrav: The Australia Research Council Centre of Excellence for Gravitational Wave Discovery

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 29 October 2025
Accepted: 18 December 2025

Abstract

Context. Pulsar timing arrays (PTAs) have recently reported compelling evidence for the presence of a gravitational-wave background signal. Mapping the gravitational-wave background is key to understanding how it is formed, since anisotropy is a tracer for, for example, a supermassive black hole binary origin.

Aims. In this work we refine the frequentist regularised gravitational-wave mapping analysis developed in our previous work (as part of the MeerKAT PTA 4.5-year data release). We derive a point-spread function describing the angular resolution of a PTA.

Methods. We investigate how the point spread function changes for different PTA constellations and determine the best possible angular resolution achievable within our framework. Using simulated data, we demonstrate that previous methods do not capture the actual resolution - especially in regions of the sky with a high density of pulsars.

Results. We propose an improved scheme that accounts for a variable local resolution and test it using realistic simulations of the latest MeerKAT dataset. We demonstrate that we are able to identify a continuous gravitational wave signal in a region with good pulsar sky coverage with approximately a factor of two increase in significance compared to our previous method.