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 Ly alpha 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 similar to 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 H i 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 H i regions, allowing them to effectively 'hide' among the many dark spectral patches and (3) modelling the Ly alpha 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 similar to 6 to even the 10 per cent level. At z similar to 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 Ly beta forest. We conclude with the caution against overinterpreting the observations. There is currently no direct evidence that reionization was complete by z similar to 5 -6.