Optimising gravitational-wave sky maps for pulsar timing arrays

TL;DR

This work advances gravitational-wave sky mapping with pulsar timing arrays by deriving a local-PSF framework and introducing an adaptive regularised spherical-harmonics scheme that reflects the sky-specific resolution dictated by pulsar geometry. By linking the PSF to the PTA distortion matrix and maximizing the informative subspace through regularisation, the authors achieve improved localization and higher significance for anisotropic GW signals, demonstrated with MeerKAT-era simulations. The approach reduces artificial hotspots and yields more precise sky maps, with practical guidance for selecting the maximum spherical-harmonics degree and regularisation level. The methods enhance the ability to discriminate anisotropic backgrounds from isotropic noise and to target follow-up searches for individual SMBHBs, with broader applicability to future, larger PTAs.

Abstract

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. 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. 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. 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.

Figures (9)

• Figure 1: Single hot pixel seen through a 40PSR PTA with different regularisation cut-offs. The crosshair indicates the position of the hot pixel. Top: Clean map with $\ell_\mathrm{max}=8$, $s_\mathrm{reg}=15$. Bottom: Clean map with $\ell_\mathrm{max}=8$, $s_\mathrm{reg}=40$.
• Figure 2: Sky maps showing the (S/N-based) PSF of the PTA as a function of sky position. The white stars indicate the positions of the pulsars in the respective PTA. Both plots were calculated using the classic spherical harmonics expansion scheme based on the number of pulsars. Top: 40 pulsar PTA, $\ell_\mathrm{max}=5, s_\mathrm{reg}=35$. Bottom: 20 pulsar subset PTA, $\ell_\mathrm{max}=3, s_\mathrm{reg}=15$.
• Figure 3: Point spread area sky maps for the 40 pulsar isotropic PTA set-up. From left to right: $\ell_\mathrm{max} = \{6,8,10,12\}$. The white stars indicate the pulsar positions.
• Figure 4: Point spread area sky maps for the 20-pulsar sub-array of the 40 pulsar isotropic PTA set-up. From left to right: $\ell_\mathrm{max} = \{4,8,10,12\}$. The white stars indicate the pulsar positions.
• Figure 5: Minimum PSF as function of $\ell_\mathrm{max}$, for different combinations of regularisation cut-offs, $s_\mathrm{reg}$. Left: 40 PSRs. Middle: 20 PSRs. Right: Distribution of area equivalents, $A_\mathrm{nn}$, of the nearest-neighbour distances in the 40-pulsar constellation.