Recent observations of high redshift quasar spectra reveal long gaps with little flux .
A small or no detectable flux does not by itself imply the intergalactic medium ( IGM ) is neutral .
Inferring the average neutral fraction from the observed absorption requires assumptions about clustering of the IGM , which the gravitational instability model supplies .
Our most stringent constraint on the neutral fraction at z \sim 6 is derived from the mean Lyman-beta transmission measured from the z = 6.28 SDSS quasar of Becker et al .
– the neutral hydrogen fraction at mean density has to be larger than 4.7 \times 10 ^ { -4 } .
This is substantially higher than the neutral fraction of \sim 3 - 5 \times 10 ^ { -5 } at z = 4.5 - 5.7 , suggesting that dramatic changes take place around or just before z \sim 6 , even though current constraints are still consistent with a fairly ionized IGM at z \sim 6 .
These constraints translate also into constraints on the ionizing background , subject to uncertainties in the IGM temperature .
An interesting alternative method to constrain the neutral fraction is to consider the probability of having many consecutive pixels with little flux , which is small unless the neutral fraction is high .
It turns out that this constraint is slightly weaker than the one obtained from the mean transmission .
We show that while the derived neutral fraction at a given redshift is sensitive to the power spectrum normalization , the size of the jump around z \sim 6 is not .
We caution that the main systematic uncertainties include spatial fluctuations in the ionizing background , and the continuum placement .
Tests are proposed .
In particular , the sightline to sightline dispersion in mean transmission might provide a useful diagnostic .
We express the dispersion in terms of the transmission power spectrum , and develop a method to calculate the dispersion for spectra that are longer than the typical simulation box .