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 into the intergalactic medium (IGM). If the thickness of the front can be measured, it can provide a novel constraint on the ionizing spectral energy distribution (SED). 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. 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, but the thickness increases as the front approaches equilibrium in 10^8 - 10^9 years, and can eventually significantly exceed simple estimates based on the mean free path. With a high intrinsic hydrogen column density obscuring the source (log(N_H/cm^-2) >~ 19.2) or a hard power-law spectrum combined with some obscuration (e.g. dlog(F_\nu)/dlog(\nu) >~ -1.2 at log(N_H/cm^-2) >~ 18.0), the thickness of the front exceeds ~1 physical Mpc and may be measurable from the morphology of its redshifted 21cm 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 Lyman-alpha trough (where the neutral fraction is ~10^-3) underestimates the size of the HII region by a factor of >~4.