2009ApJ...706..970D

Recent observations suggest that helium became fully ionized around redshift z ∼ 3. The He II optical depth derived from the Lyα 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 of ∼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 He III 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.