Probing patchy reionization through tau-21cm correlation statistics
  We consider the cross-correlation between free electrons and neutral hydrogen
during the epoch of reionization. The free electrons are traced by the optical
depth to reionization tau, while the neutral hydrogen can be observed through
21 cm photon emission. As expected, this correlation is sensitive to the
detailed physics of reionization. Foremost, if reionization occurs through the
merger of relatively large halos hosting an ionizing source, the free electrons
and neutral hydrogen are anti-correlated for most of the reionization history.
A positive contribution to the correlation can occur when the halos that can
form an ionizing source are small. A measurement of this sign change in the
cross-correlation would directly measure the bubble bias and as, such, the halo
mass. We estimate the signal-to-noise of the cross-correlation using the
estimator for inhomogeneous reionization tau_{lm} proposed by Dvorkin and Smith
(2009). We find that with upcoming radio interferometers and CMB experiments,
the cross-correlation is measurable going up to multipoles l ~ 1000. We also
derive parameter constraints and conclude that, despite the foregrounds, the
cross-correlation proofs a complementary measurement of the EoR parameters to
the 21 cm and CMB polarization auto-correlations expected to be observed in the
coming decade.
