Tom Theuns

An ionization front (I-front) that propagates through an inhomogeneous medium is slowed down by self-shielding and recombinations. We perform cosmological radiation hydrodynamics simulations of the I-front propagation during the epoch of cosmic reionization. The simulations resolve gas in mini-haloes (halo mass 104 ≲ Mh[M⊙] ≲ 108) that could dominate recombinations, in a computational volume that is large enough to sample the abundance of such haloes. The numerical resolution is sufficient (gas-particle mass ∼20 M⊙ and spatial resolution <0.1 ckpc) to allow accurate modelling of the hydrodynamic response of gas to photoheating. We quantify the photoevaporation time of mini-haloes as a function of Mh and its dependence on the photoionization rate, Γ−12, and the redshift of reionization, zi. The recombination rate can be enhanced over that of a uniform medium by a factor ∼10−20 early on. The peak value increases with Γ−12 and decreases with zi, due to the enhanced contribution from mini-haloes. The clumping factor, cr, decreases to a factor of a few at ∼100 Myr after the passage of the I-front when the mini-haloes have been photoevaporated; this asymptotic value depends only weakly on Γ−12. Recombinations increase the required number of photons per baryon to reionize the Universe by 20 per cent–100 per cent, with the higher value occurring when Γ−12 is high and zi is low. We complement the numerical simulations with simple analytical models for the evaporation rate and the inverse Strömgren layer. The study also demonstrates the proficiency and potential of sph-m1rt to address astrophysical problems in high-resolution cosmological simulations.

We present an analytical model for cosmological Lyman-limit systems (lls) that successfully reproduces the observed evolution of the mean free path (λeff) of ionizing photons. The evolution of the co-moving mean free path is predominantly a consequence of the changing meta galactic photoionization rate and the increase with cosmic time of the minimum mass below which haloes lose their gas due to photoheating. In the model, Lyman-limit absorption is caused by highly ionized gas in the outskirt of dark matter haloes. We exploit the association with haloes to compute statistical properties of λeff and of the bias, b, of lls. The latter increases from b ∼ 1.5 → 2.6 from redshifts z = 2 → 6. Combined with the rapid increase with redshift of the bias of the haloes that host a quasar, the model predicts a rapid drop in the value of λeff when measured in quasar spectra from z = 5 → 6, whereas the actual value of λeff falls more smoothly. We derive an expression for the effective optical depth due to Lyman limit absorption as a function of wavelength and show that it depends sensitively on the poorly constrained number density of lls as a function of column density. The optical depth drops below unity for all wavelengths below a redshift of ∼2.5 which is therefore the epoch when the Universe first became transparent to ionizing photons.