AGN-driven helium reionization and the incidence of extended HeIII
  regions at redshift z>3
  We use hydrodynamic simulations post-processed with the radiative-transfer
code RADAMESH to assess recent claims that the low HeII opacity observed in z>3
quasar spectra may be incompatible with models of HeII reionization driven by
the observed population of active galactic nuclei (AGNs). In particular,
building upon our previous work, we consider an early population of sources and
start the radiative-transfer calculation at redshifts z>=5. Our model
faithfully reproduces the emissivity of optically selected AGNs as inferred
from measurements of their luminosity function. We find that HeII reionization
is very extended in redshift ({\Delta} z>=2) and highly spatially
inhomogeneous. In fact, mock spectra extracted from the simulations show a
large variability in the evolution of the HeII effective optical depth within
chunks of size {\Delta} z=0.04. Regions with low opacity
({\tau}^{eff}_{HeII}<3) can be found at high redshift, in agreement with the
most recent observations of UV-transmitting quasars. At the highest redshift
currently probed by observations (z~3.4), our updated model predicts a much
lower HeII effective optical depth than previous simulations in the literature
relieving most of the tension with the current data, that, however, still
persists at about the (Gaussian) 1{\sigma} to 2{\sigma} level. Given the very
small number of observed lines of sight, our analysis indicates that current
data cannot rule out a purely AGN-driven scenario with high statistical
significance.
