Reionization bias in high-redshift quasar near-zones

Absorption spectra of high-redshift quasars exhibit an increasingly thick Lyα forest, suggesting that the fraction of neutral hydrogen in the intergalactic medium (IGM) is increasing towards z ∼ 6. However, the interpretation of these spectra is complicated by the fact that the Lyα optical depth is already large for neutral hydrogen fractions in excess of 10^-4, and also because quasars are expected to reside in dense regions of the IGM. We present a model for the evolution of the ionization state of the IGM which is applicable to the dense, biased regions around high-redshift quasars as well as more typical regions in the IGM. We employ a cold dark matter based model in which the ionizing photons for reionization are produced by star formation in dark matter haloes spanning a wide range of masses, combined with numerical radiative transfer simulations which model the resulting opacity distribution in quasar absorption spectra. With an appropriate choice for the parameter which controls the star formation efficiency, our model is able to simultaneously reproduce the observed Lyα forest opacity at 4 < z < 6, the ionizing photon mean-free-path at z ∼ 4 and the rapid evolution of highly ionized near-zone sizes around high-redshift quasars at 5.8 < z < 6.4. In our model, reionization extends over a wide redshift range, starting at z ≳ 10 and completing as H ii regions overlap at z ∼ 6-7. We find that within 5 physical Mpc of a high-redshift quasar, the evolution of the ionization state of the IGM precedes that in more typical regions by around 0.3 redshift units. More importantly, when combined with the rapid increase in the ionizing photon mean-free-path expected shortly after overlap, this offset results in an ionizing background near the quasar which exceeds the value in the rest of the IGM by a factor of ∼2-3. We further find that in the post-overlap phase of reionization the size of the observed quasar near-zones is not directly sensitive to the neutral hydrogen fraction of the IGM. Instead, these sizes probe the level of the background ionization rate and the temperature of the surrounding IGM. The observed rapid evolution of the quasar near-zone sizes at 5.8 < z < 6.4 can thus be explained by the rapid evolution of the ionizing background, which in our model is caused by the completion of overlap at the end of reionization by 6 ≲ z ≲ 7.