How Neutral is the Intergalactic Medium at z ~ 6?

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 ~ 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 $3.4 \times 10^{-4}$. This is substantially higher than the neutral fraction of $\sim 2-5 \times 10^{-5}$ at z = 4.5 - 5.7, suggesting that dramatic changes take place around z ~ 6, even though current constraints are consistent with a fairly ionized IGM at z ~ 6. An interesting alternative method to constrain the neutral fraction is to make use of the Lyman-beta Gunn-Peterson trough itself -- the fact that a long stretch of spectrum exhibits no large upward fluctuations in transmission implies an upper limit on the neutral fraction, which turns out to be comparable to 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 ~ 6 is not. We caution that the main systematic uncertainties include spatial fluctuations in the ionizing background, and the continuum placement. Tests are proposed. The sightline dispersion in mean transmission may provide a useful diagnostic. We express the dispersion in terms of the transmission power spectrum, and develop a way to predict the dispersion for spectra that are longer than the typical simulation box.