What do observations of the Lyman α 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 (Ly) fraction, the percentage of Lyman-break selected galaxies that emit appreciably in the Ly line. This fraction is expected to fall-off towards high redshift as the intergalactic medium becomes significantly neutral, and the galaxies' Ly emission is progressively attenuated. Intriguingly, early measurements with this technique suggest a strong drop in the Ly fraction near z 7. Previous work concluded that this requires a surprisingly neutral intergalactic medium -with neutral hydrogen filling more than 50 per cent of the volume of the Universe -at this redshift. We model the evolving Ly fraction using cosmological simulations of the reionization process. Before reionization completes, the simulated Ly fraction has large spatial fluctuations owing to the inhomogeneity of reionization. Since existing measurements of the Ly 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 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 H I 0.05 at 95 per cent confidence level. Hence, we find that the z 7 Ly fraction measurements do likely probe the Universe before reionization completes but that they do not require a very large neutral fraction.