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 that 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 Lyβ transmission measured from the z = 6.28 Sloan Digital Sky Survey quasar of Becker and coworkers; the neutral hydrogen fraction at mean density has to be larger than 4.7 × 10^-4. This is substantially higher than the neutral fraction of ∼(3-5)×10^-5 at z = 4.5-5.7, suggesting that dramatic changes take place around or just before z ∼ 6, even though current constraints are still consistent with a fairly ionized IGM at z ∼ 6. These constraints also translate 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 ∼ 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 sight line-to-sight line 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.