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

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 dₚᵤₗₛₐᵣ can characterize up to $2N/7$ distant chirping sources per frequency bin Δfgw=1/T and localize them with ``diffraction-limited'' precision δθ(1/SNR)(λgw/dₚᵤₗₛₐᵣ). Even if the pulsar distances are poorly known, a PTA with F GW frequency bins can still characterize up to (2N/7)(1-1/2F) 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 δθ(1/SNR)√λgw/dₚᵤₗₛₐᵣ. 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.