We use a set of cosmological simulations combined with radiative transfer calculations to investigate the distribution of neutral hydrogen in the post-reionization Universe. We assess the contributions from the metagalactic ionizing background, collisional ionization and diffuse recombination radiation to the total ionization rate at redshifts z = 0 − 5. We find that the densities above which hydrogen self-shielding becomes important are consistent with analytic calculations and previous work. However, because of diffuse recombination radiation, whose intensity peaks at the same density, the transition between highly ionized and self-shielded regions is smoother than what is usually assumed. We provide fitting functions to the simulated photoionization rate as a function of density and show that post-processing simulations with the fitted rates yields results that are in excellent agreement with the original radiative transfer calculations. The predicted neutral hydrogen column density distributions agree very well with the observations. In particular, the simulations reproduce the remarkable lack of evolution in the column density distribution of Lyman limit and weak damped Lyα systems below z = 3. The evolution of the low column density end is affected by the increasing importance of collisional ionization with decreasing redshift. On the other hand, the simulations predict the abundance of strong damped Lyα systems to broadly track the cosmic star formation rate density.

The critical star formation rate (SFR) density required to keep the intergalactic hydrogen ionized depends crucially on the average rate of recombinations in the intergalactic medium (IGM). This rate is proportional to the clumping factor C≡〈ρ2b〉IGM/〈ρb〉2, where ρb and 〈ρb〉 are the local and cosmic mean baryon density, respectively, and the brackets 〈〉IGM indicate spatial averaging over the recombining gas in the IGM. We perform a suite of cosmological smoothed particle hydrodynamic simulations that include radiative cooling to calculate the volume‐weighted clumping factor of the IGM at redshifts z≥ 6. We focus on the effect of photoionization heating by a uniform ultraviolet background and find that photoheating strongly reduces the clumping factor because the increased pressure support smoothes out small‐scale density fluctuations. Photoionization heating is often said to provide a negative feedback on the re‐ionization of the IGM because it suppresses the cosmic SFR by boiling the gas out of low‐mass haloes. However, because of the reduction of the clumping factor it also makes it easier to keep the IGM ionized. Photoheating therefore also provides a positive feedback which, while known to exist, has received much less attention. We demonstrate that this positive feedback is in fact very strong. Using conservative assumptions, we find that if the IGM was reheated at z≳ 9, the observed population of star‐forming galaxies at z≈ 6 may be sufficient to keep the IGM ionized, provided that the fraction of ionizing photons that escape the star‐forming regions to ionize the IGM is larger than ∼0.2.

We present measurements of the specific ultraviolet luminosity density from a sample of 483 galaxies at 6 z 8. These galaxies were selected from new deep near-infrared Hubble Space Telescope imaging from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey, Hubble UltraDeep Field 2009 and WFC3 Early Release Science programs. In contrast to the majority of previous analyses, which assume that the distribution of galaxy ultraviolet (UV) luminosities follows a Schechter distribution, and that the distribution continues to luminosities far below our observable limit, we investigate the contribution to reionization from galaxies which we can observe, free from these assumptions. Due to our larger survey volume, wider wavelength coverage, and updated assumptions about the clumping of gas in the intergalactic medium (IGM), we find that the observable population of galaxies can sustain a fully reionized IGM at z = 6, if the average ionizing photon escape fraction (f esc ) is ∼30%. A number of previous studies have measured UV luminosity densities at these redshifts that vary by a factor of 5, with many concluding that galaxies could not complete reionization by z = 6 unless a large population of galaxies fainter than the detection limit were invoked, or extremely high values of f esc were present. The observed UV luminosity density from our observed galaxy samples at z = 7 and 8 is not sufficient to maintain a fully reionized IGM unless f esc > 50%. We examine the contribution from galaxies in different luminosity ranges, and find that the sub-L * galaxies we detect are stronger contributors to the ionizing photon budget than the L > L * population, unless f esc is luminosity dependent. Combining our observations with constraints on the emission rate of ionizing photons from Lyα forest observations at z = 6, we find that we can constrain f esc < 34% (2σ) if the observed galaxies are the only contributors to reionization, or < 13% (2σ) if the luminosity function extends to a limiting magnitude of M UV = −13. These escape fractions are sufficient to complete reionization by z = 6. Current constraints on the high-redshift galaxy population imply that the volume ionized fraction of the IGM, while consistent with unity at z ≤ 6, appears to drop at redshifts not much higher than 7, consistent with a number of complementary reionization probes. If faint galaxies dominated the ionizing photon budget at z = 6-7, future extremely deep observations with the James Webb Space Telescope will probe deep enough to see them, providing an indirect constraint on the global ionizing photon escape fraction.

We present traphic, a novel radiative transfer scheme for smoothed particle hydrodynamics (SPH) simulations. traphic is designed for use in simulations exhibiting a wide dynamic range in physical length‐scales and containing a large number of light sources. It is adaptive both in space and in angle and can be employed for application on distributed memory machines. The commonly encountered computationally expensive scaling with the number of light sources in the simulation is avoided by introducing a source merging procedure. The (time‐dependent) radiative transfer equation is solved by tracing individual photon packets in an explicitly photon‐conserving manner directly on the unstructured grid traced out by the set of SPH particles. To accomplish directed transport of radiation despite the irregular spatial distribution of the SPH particles, photons are guided inside cones. We present and test a parallel numerical implementation of traphic in the SPH code gadget‐2, specified for the transport of monochromatic hydrogen‐ionizing radiation. The results of the tests are in excellent agreement with both analytic solutions and results obtained with other state‐of‐the‐art radiative transfer codes.

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