Realistic assessment of a single gravitational wave source localization taking into account precise pulsar distances with pulsar timing arrays

TL;DR

This paper tackles the challenge of localizing a single CGW source with a pulsar timing array by incorporating precise pulsar distance measurements. It develops a closed-form, analytic Bayesian framework to compute posterior contours for the GW sky location, exploiting distance priors and the pulsar-term phase information. The key finding is that SKA-era distance precisions for nearby pulsars can reduce the localization area to ~$10^{-3}$ deg$^{2}$, especially when the GW source lies near well-measured pulsars, whereas current distance uncertainties leave localization far from this target. The work also clarifies how PTA geometry and noise levels govern localization improvements and outlines future work to handle non-linearities, stochastic signals, and realistic timing models. This has practical implications for identifying host galaxies and enabling targeted electromagnetic follow-ups of SMBHBs.

Abstract

Pulsar timing arrays (PTAs) are anticipated to detect continuous gravitational waves (GWs) from individual supermassive black hole binaries (SMBHBs) in the near future. To identify the host galaxy of a GW source, PTAs require significantly improved angular resolution beyond the typical range of 100-1000 square degrees achieved by recent continuous GW searches. In this study, we investigate how precise pulsar distance measurements can enhance the localization of a single GW source. Accurate distance information, comparable to or better than the GW wavelength (typically 1~pc) can refine GW source localization. In the near future, with the advent of Square Kilometre Array (SKA), such high-precision distance measurements will be feasible for a few nearby pulsars. We focus on the relatively nearby pulsars J0437-4715 (156 pc) and J0030+0451 (331 pc), incorporating their actual distance uncertainties based on current VLBI measurements and the anticipated precision of the SKA-era. By simulating 87 pulsars with the GW signal and Gaussian white noise in the timing residuals, we assess the impact of the pulsar distance information on GW source localization. Our results show that without precise distance information, localization remains insufficient to identify host galaxies under 10 ns noise. However, incorporating SKA-era distance precision for nearby pulsars J0437-4715 and J0030+0451 can reduce localization uncertainties to the required level of $10^{-3}$ $\rm deg^{2}$. Localization accuracy strongly depends on the geometric configuration of pulsars with well-measured distances and improves notably near and between such pulsars. The improvement of the localization will greatly aid in identifying the host galaxy of a GW source and constructing an SMBHB catalog. It will further enable follow-up electromagnetic observations to investigate the SMBHB in greater detail.

Figures (6)

• Figure 1: Sky locations of the pulsars, where the star markers denote the sky locations of the pulsars. The two pulsars of interest (J0030+0451 and J0437-4715) are highlighted with larger star markers.
• Figure 2: Areas $\Omega$ of the two-dimensional 68% contour of the GW sky location ($\theta$ and $\phi$) as a function of the GW sky location in the fiducial case described in \ref{['distance prior']}. The CGW parameters used correspond to the slow evolution case listed in \ref{['parameters']}. From left to right, the standard deviations of the white noise are 10, 30, and 100 ns, respectively. Each GW sky location is located at the center of each pixel. Star markers denote the sky locations of the pulsars.
• Figure 3: Same as \ref{['fig:contour_noinfo']}, except that from top to bottom, the rows correspond to fiducial case and Cases 1, 2 and 3 in \ref{['distance prior']}. The same color bar is used for each column.
• Figure 4: Contours for GW sources located between J0437-4715 and J0030+0451. The CGW signal parameters used are those of the slow evolution case shown in \ref{['parameters']}. The outer contour (green dashed line) corresponds to the fiducial case, while the inner contour (blue solid line) corresponds to Case 3 in \ref{['distance prior']}. The contour corresponds to the $(1 - 10^{-15}) \times 100\%$ confidence level for clarity.
• Figure 5: Left panel: The source numbers corresponding to the contours in \ref{['fig:contour_geodesic_zoom']}. Right panel: Areas $\Omega$ of the two-dimensional 68% contours for GW sources located between J0437-4715 and J0030+0451. Source 14 is the same as Source 5. The green lines correspond to the fiducial case, while the blue lines correspond to Case 3. The solid, dashed, and dash-dotted lines correspond to the Slow, Fast, and No evolution cases in \ref{['parameters']}, respectively.