Constraining Reionization with the Evolution of the Luminosity Function   of Lyman Alpha mitting Galaxies
  At redshifts beyond z>6, as the mean fraction of neutral hydrogen x_HI in the intergalactic medium (IGM) increases, the line flux of Lyman alpha (Lya) emitters can be significantly suppressed, which can result in a decrease in the observed number of emitters at a given Lya flux. However, cosmological HII regions surrounding the Lya emitting galaxies alleviate these effects. We use simple models of the Lya line suppression that incorporate the presence of HII regions to predict the overall effect of the Lya absorption on the Lya luminosity function. We find, in agreement with other recent studies, that unless ionizing sources are unusually strongly clustered, a fully neutral IGM may be inconsistent with the large abundance of confirmed z=6.5 Lya emitters. However, the presence of local HII regions prohibits placing a tight constraint on the mean neutral fraction. We find x_HI < 0.25; the presence of strong winds and/or the clustering of ionizing sources would further weaken this constraint. We conclude that the evolution of the Lya LF is consistent with reionization occurring near this redshift. Finally, we suggest that a measurement of observed Lya line width as a function of the Lya luminosity, in a future, larger sample of Lya emitters, may serve as a robust diagnostic of the neutral fraction in the IGM. 
Zoltan Haiman (Columbia University), Renyue Cen (Princeton University)