The thickness of high‐redshift quasar ionization fronts as a constraint on the ionizing spectral energy distribution

High‐redshift quasars ( z ≳ 6) drive ionization fronts (I‐fronts) into the intergalactic medium (IGM), with the thickness of the front generally increasing with the hardness of ionizing spectrum. If the thickness of the front can be measured, it can provide a novel constraint on the ionizing spectral energy distribution, uniquely available for sources prior to the end of reionization. Here we follow the propagation of an I‐front into a uniform IGM, and compute its thickness for a range of possible quasar spectra and ages, and IGM neutral hydrogen densities and clumping factors. We also explore the effects of uniform and non‐uniform ionizing backgrounds. We find that even for hard spectra, the fronts are initially thin, with a thickness much smaller than the mean free path of ionizing photons. The front gradually thickens as it approaches equilibrium in 10 8 –10 9 yr, and the thickness of its outer part can eventually significantly exceed simple estimates based on the mean free path. With a sufficiently high intrinsic hydrogen column density obscuring the source [log( N H /cm −2 ≳ 19.2] or a sufficiently hard power‐law spectrum combined with some obscuration [e.g. d log  F ν /d log ν≳−1.2 at log( N H /cm −2 ) ≳ 18.0 ], the outer thickness of the front exceeds ∼1 physical Mpc and may be measurable from the 3D morphology of its redshifted 21‐cm signal. We find that the highly ionized inner part of the front, which may be probed by Lyman‐line absorption spectra, remains sharp for bright quasars unless a large obscuring column [log( N H /cm −2 ) ≳ 19.2] removes most of their ionizing photons up to ≈40 eV. For obscured sources with log( N H /cm −2 ) ≳ 19.8 , embedded in a significantly neutral IGM, the black Lyα trough (where the neutral fraction is ∼10 −3 ) underestimates the size of the H  ii region by a factor of ≳4.