We investigate the potential of exploiting Ly \alpha Emitters ( LAEs ) to constrain the volume-weighted mean neutral hydrogen fraction of the IGM , \bar { x } _ { HI } , at high redshifts ( specifically z \sim 9 ) .
We use “ semi-numerical ” simulations to efficiently generate density , velocity , and halo fields at z = 9 in a 250 Mpc box , resolving halos with masses M \geq 2.2 \times 10 ^ { 8 } M _ { \odot } .
We construct ionization fields corresponding to various values of \bar { x } _ { HI } .
With these , we generate LAE luminosity functions and “ counts-in-cell ” statistics .
As in previous studies , we find that LAEs begin to disappear rapidly when \bar { x } _ { HI } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt% \hbox { $ > $ } } 0.5 .
Constraining \bar { x } _ { HI } ( z = 9 ) with luminosity functions is difficult due to the many uncertainties inherent in the host halo mass \leftrightarrow Ly \alpha luminosity mapping .
However , using a very conservative mapping , we show that the number densities derived using the six z \sim 9 LAEs recently discovered by Stark et al .
( 2007 ) imply \bar { x } _ { HI } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt% \hbox { $ < $ } } 0.7 .
On a more fundamental level , these LAE number densities , if genuine , require substantial star formation in halos with M \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ < $ } } 10 ^ { % 9 } M _ { \odot } , making them unique among the current sample of observed high- z objects .
Furthermore , reionization increases the apparent clustering of the observed LAEs .
We show that a “ counts-in-cell ” statistic is a powerful probe of this effect , especially in the early stages of reionization .
Specifically , we show that a field of view ( typical of upcoming IR instruments ) containing LAEs has \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ > $ } } 10 % higher probability of containing more than one LAE in a \bar { x } _ { HI } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt% \hbox { $ > $ } } 0.5 universe than a \bar { x } _ { HI } \approx 0 universe with the same overall number density .
With this statistic , an ionized universe can be robustly distinguished from one with \bar { x } _ { HI } \ga 0.5 using a survey containing only \sim 20–100 galaxies .