Pulsar-timing measurement of the circular polarization of the stochastic
  gravitational-wave background
  Pulsar-timing arrays (PTAs) are in the near future expected to detect a
stochastic gravitational-wave background (SGWB) produced by a population of
inspiralling super-massive black hole binaries. In this work, we consider a
background that can be anisotropic and circularly polarized. We use the
expansion of the intensity and the circular polarization in terms of spherical
harmonics and the overlap reduction functions for each term in this expansion.
We propose an unbiased real-space estimator that can separate the intensity and
circular-polarization contributions of the SGWB to pulsar-timing-residual
correlations and then validate the estimator on simulated data. We compute the
signal-to-noise ratio of a circular-polarization component that has a dipole
pattern under different assumptions about the PTA. We find that a
nearly-maximal circular-polarization dipole may be detectable, which can aid in
determining whether or not the background is dominated by a handful of bright
sources.
