How to Search for Islands of Neutral Hydrogen in the $z \sim 5.5$ IGM
  Observations of the Lyman-alpha (Ly-$\alpha$) forest may allow reionization
to complete as late as $z \sim 5.5$, provided the ionization state of the
intergalactic medium (IGM) is sufficiently inhomogeneous at these redshifts. In
this case, significantly neutral islands may remain amongst highly ionized gas
with the ionized regions allowing some transmission through the Ly-$\alpha$
forest. This possibility has the important virtue that it is eminently testable
with existing Ly-$\alpha$ forest data. In particular, we describe three
observable signatures of significantly neutral gas in the $z \sim 5.5$ IGM. We
use mock quasar spectra produced from numerical simulations of reionization to
develop these tests. First, we quantify how the abundance and length of
absorbed regions in the forest increase with the volume-averaged neutral
fraction in our reionization model. Second, we consider stacking the
transmission profile around highly absorbed regions in the forest. If and only
if there is significantly neutral gas in the IGM, absorption in the damping
wing of the Ly-$\alpha$ line will cause the transmission to recover slowly as
one moves from absorbed to transmitted portions of the spectrum. Third, the
deuterium Ly-$\beta$ line should imprint a small but distinctive absorption
feature slightly blueward of absorbed neutral regions in the Ly-$\beta$ forest.
We show that these tests can be carried out with existing Keck HIRES spectra at
$z \sim 5.5$, with the damping wing being observable for $< x_{\text{HI}}
>\gtrsim 0.05$ and the deuterium feature observable with additional
high-resolution spectra for $< x_{\text{HI}} >\gtrsim 0.2$.
