  Recent observations suggest that helium became fully ionized around redshift
z ~ 3. The HeII optical depth derived from the Lyman-alpha forest decreases
substantially from this period to z ~ 2; moreover, it fluctuates strongly near
z ~ 3 and then evolves smoothly at lower redshifts. From these opacities, we
compute, using a semi-analytic model, the evolution of the mean photoionization
rate and the attenuation length for helium over the redshift range 2.0 < z <
3.2. This model includes an inhomogeneous metagalactic radiation background,
which is expected during and after helium reionization. We find that assuming a
uniform background underestimates the required photoionization rate by up to a
factor ~2. When averaged over the (few) available lines of sight, the effective
optical depth exhibits a discontinuity near z = 2.8, but the measurement
uncertainties are sizable. This feature translates into a jump in the
photoionization rate and, provided the quasar emissivity evolves smoothly, in
the effective attenuation length, perhaps signaling the helium reionization
era. We then compute the evolution of the effective optical depth for a variety
of simple helium reionization models, in which the measured quasar luminosity
function and the attenuation length, as well as the evolving HeIII fraction,
are inputs. A model with reionization ending around redshift z ~ 2.7 is most
consistent with the data, although the constraints are not strong thanks to the
sparseness of the data.
