What do observations of the Lyman-alpha fraction tell us about
  reionization?
  An appealing approach for studying the reionization history of the Universe
is to measure the redshift evolution of the Lyman-alpha fraction, the
percentage of Lyman-break selected galaxies that emit appreciably in the
Ly-alpha line. This fraction is expected to fall-off towards high redshift as
the intergalactic medium becomes significantly neutral, and the galaxies'
Ly-alpha emission is progressively attenuated. Intriguingly, early measurements
with this technique suggest a strong drop in the Ly-alpha fraction near z ~ 7.
Previous work concluded that this requires a surprisingly neutral intergalactic
medium -- with neutral hydrogen filling more than 50 % of the volume of the
Universe -- at this redshift. We model the evolving Ly-alpha fraction using
cosmological simulations of the reionization process. Before reionization
completes, the simulated Ly-alpha fraction has large spatial fluctuations owing
to the inhomogeneity of reionization. Since existing measurements of the
Ly-alpha fraction span relatively small regions on the sky, and sample these
regions only sparsely, they may by chance probe mostly galaxies with above
average Ly-alpha attenuation. We find that this sample variance is not
exceedingly large for existing surveys, but that it does somewhat mitigate the
required neutral fraction at z ~ 7. Quantitatively, in a fiducial model
calibrated to match measurements after reionization, we find that current z = 7
observations require a volume-averaged neutral fraction of x_HI > 0.05 at 95 %
confidence level. Hence, we find that the z ~ 7 Ly-alpha fraction measurements
do likely probe the Universe before reionization completes but that they do not
require a very large neutral fraction.
