Was reionization complete by z ~ 5-6?

It is generally taken for granted that reionization has completed by z = 6, due to the detection of flux in the Lyα forest at redshifts z < 6. However, since reionization is expected to be highly inhomogeneous, much of the spectra pass through just the ionized component of the intergalactic medium (IGM) even for non-negligible values of the volume-weighted mean neutral hydrogen fraction, . We study the expected signature of an incomplete reionization at z ~ 5 -6, using very large-scale (2 Gpc) seminumeric simulations. We find that ruling out an incomplete reionization is difficult at these redshifts since: (1) quasars reside in biased regions of the ionization field, with fewer surrounding HI patches than implied by the global mean, ; this bias extends tens of comoving megaparsecs for ; (2) absorption from the residual neutral hydrogen inside the ionized IGM generally dominates over the absorption from the remaining HI regions, allowing them to effectively `hide' among the many dark spectral patches and (3) modelling the Lyα forest and its redshift evolution even in just the ionized IGM is very difficult, and nearly impossible to do a priori. We propose using the fraction of pixels which are dark as a simple, nearly model-independent upper limit on . Alternately, the size distribution of regions with no detectable flux (dark gaps) can be used to place a more model-dependent constraint. Either way, the current sample of quasars is statistically insufficient to constrain at z ~ 6 to even the 10 per cent level. At z ~ 5, where there are more available sightlines and the forest is less dark, constraining might be possible given a large dynamic range from very deep spectra and/or the Lyβ forest. We conclude with the caution against overinterpreting the observations. There is currently no direct evidence that reionization was complete by z ~ 5 -6.