THE EVOLUTION OF THE HELIUM-IONIZING BACKGROUND AT z ∼ 2-3

Recent observations suggest that helium became fully ionized around redshift z similar to 3. The He II optical depth derived from the Ly alpha forest decreases substantially from this period to z similar to 2; moreover, it fluctuates strongly near z similar to 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 less than or similar to z less than or similar to 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 similar to 2. When averaged over the (few) available lines of sight, the effective optical depth exhibits a discontinuity near z approximate to 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 approximate to 2.7 is most consistent with the data, although the constraints are not strong thanks to the sparseness of the data.