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

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 ${d}_{\mathrm{pulsar}}$ can characterize up to $2N/7$ distant chirping sources per frequency bin $\ensuremath{\Delta}{f}_{\mathrm{gw}}=1/T$ and localize them with ``diffraction-limited'' precision $\ensuremath{\delta}\ensuremath{\theta}\ensuremath{\gtrsim}(1/\mathrm{SNR})({\ensuremath{\lambda}}_{\mathrm{gw}}/{d}_{\mathrm{pulsar}})$. Even if the pulsar distances are poorly known, a PTA with $F$ GW frequency bins can still characterize up to $(2N/7)(1\ensuremath{-}\frac{1}{2F})$ sources per bin, and the quasisingular pattern of timing residuals in the vicinity of a GW source still allows the source to be localized quasitopologically within roughly the smallest quadrilateral of quiet pulsars that encircles it on the sky, down to a limiting resolution $\ensuremath{\delta}\ensuremath{\theta}\ensuremath{\gtrsim}(1/\mathrm{SNR})\sqrt{{\ensuremath{\lambda}}_{\mathrm{gw}}/{d}_{\mathrm{pulsar}}}$. PTAs may be unconfused, even at the lowest GW frequencies: in that case, standard analysis techniques designed to detect a stochastic GW background would be incomplete and suboptimal, whereas matched filtering could provide more information and sensitivity.