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 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 greater than or similar to (1/SNR)(lambda(gw)/d(pulsar)). 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 delta theta greater than or similar to (1/SNR)root lambda(gw)/d(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.