Pulsar timing arrays as imaging gravitational wave telescopes: angular resolution and source (de)confusion

TL;DR

Pulsar timing arrays can act as high-resolution gravitational wave telescopes, capable of detecting and localizing multiple sources with diffraction-limited precision, even with limited pulsar distance knowledge.

Contribution

This paper introduces a novel framework for using PTAs as imaging GW telescopes, detailing their angular resolution and source confusion limits.

Findings

PTAs can localize GW sources with diffraction-limited precision.

Even with poorly known pulsar distances, PTAs can characterize multiple sources.

Matched filtering remains effective at low frequencies.

Abstract

Pulsar timing arrays (PTAs) will be sensitive to a finite number of gravitational wave (GW) "point" sources (e.g. supermassive black hole binaries). N quiet pulsars with accurately known distances d_{pulsar} can characterize up to 2N/7 distant chirping sources per frequency bin \Delta f_{gw}=1/T, and localize them with "diffraction limited" precision \delta\theta \gtrsim (1/SNR)(\lambda_{gw}/d_{pulsar}). Even if the pulsar distances are poorly known, a PTA with F frequency bins can still characterize up to (2N/7)[1-(1/2F)] sources per bin, and the quasi-singular pattern of timing residuals in the vicinity of a GW source still allows the source to be localized quasi-topologically within roughly the smallest quadrilateral of quiet pulsars that encircles it on the sky, down to a limiting resolution \delta\theta \gtrsim (1/SNR) \sqrt{\lambda_{gw}/d_{pulsar}}. PTAs may be unconfused, even at the lowest frequencies, with matched filtering always appropriate.