Neutral hydrogen around high-z QSO and an optical depth tau ~ 0.17 can be
reconciled if reionization is more complex than a single transition at z ~ 6-8.
Tracing its details could shed a new light on the first sources of radiation.
Here we discuss how far such details can be inspected through planned
experiments on CMB large-scale anisotropy and polarization, by simulating an
actual data analysis. By considering a set of double reionization histories of
Cen (2003) type, a relevant class of models not yet considered by previous
works, we confirm that large angle experiments rival high resolution ones in
reconstructing the reionization history. We also confirm that reionization
histories, studied with the prior of a single and sharp reionization, yield a
biased tau, showing that this bias is generic. We further find a monotonic
trend in the bias for the models that we consider, and propose an explanation
of the trend, as well as the overall bias. We also show that in long-lived
experiments such a trend can be used to discriminate between single and double
reionization patterns.Comment: 8 pages, 11 figures. Substantial rewriting, replaced with accepted
version. To be published in A&