Pulsar timing array observations of gravitational wave source timing
  parallax
  Pulsar timing arrays act to detect gravitational waves by observing the
small, correlated effect the waves have on pulse arrival times at Earth. This
effect has conventionally been evaluated assuming the gravitational wave
phasefronts are planar across the array, an assumption that is valid only for
sources at distances $R\gg2\pi{}L^2/\lambda$, where $L$ is physical extent of
the array and $\lambda$ the radiation wavelength. In the case of pulsar timing
arrays (PTAs) the array size is of order the pulsar-Earth distance (kpc) and
$\lambda$ is of order pc. Correspondingly, for point gravitational wave sources
closer than $\sim100$~Mpc the PTA response is sensitive to the source parallax
across the pulsar-Earth baseline. Here we evaluate the PTA response to
gravitational wave point sources including the important wavefront curvature
effects. Taking the wavefront curvature into account the relative amplitude and
phase of the timing residuals associated with a collection of pulsars allows us
to measure the distance to, and sky position of, the source.
