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

Understand

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}}.