Updated dark pixel fraction constraints on reionization’s end from the Lyman-series forests of XQR−30

The fraction of ‘dark pixels’ in the Lyα and other Lyman-series forests at z ~ 5–6 provides a powerful constraint on the end of the reionization process. Any spectral region showing transmission must be highly ionized, while dark regions could be ionized or neutral, thus the dark pixel fraction provides a (nearly) model independent upper limit to the volume-filling fraction of the neutral intergalactic medium, modulo choices in binning scale and dark pixel definition. Here, we provide updated measurements of the 3.3comoving Mpc dark pixel fraction at z = 4.85–6.25 in the Lyα, Lyβ, and Lyγ forests of 34 deep 5.8 ≲ z ≲ 6.6 quasar spectra from the (enlarged) XQR−30 sample. Using the negative pixel method to measure the dark pixel fraction, we derive fiducial 1σ upper limits on the volume-average neutral hydrogen fraction of (x_HI) ≤ (0.030 + 0.048, 0.095 + 0.037, 0.191+0.056, 0.199 + 0.087) at z = (5.481, 5.654, 5.831, 6.043) from the optimally sensitive combination of the Lyβ and Lyγ forests. We further demonstrate an alternative method that treats the forest flux as a mixture of dark and transparent regions, where the latter are modelled using a physically motivated parametric form for the intrinsic opacity distribution. The resulting model-dependent upper limits on (x_HI) are similar to those derived from our fiducial model-independent analysis. We confirm that the bulk of reionization must be finished at z > 6, while leaving room for an extended ‘soft landing’ to the reionization history down to z ~ 5.4 suggested by Lyσ forest opacity fluctuations.