Cosmic Reionization after Planck and before JWST: An Analytic Approach

The reionization of cosmic hydrogen marks a critical juncture in the history of structure formation. Here we present a new formulation of the standard reionization equation for the evolution of the volume-averaged H ii fraction that is more consistent with the accepted conceptual model of inhomogeneous intergalactic absorption. The revised equation explicitly accounts for the presence of the optically thick "Lyman-limit systems" that are known to determine the mean-free path of ionizing radiation after overlap. Integration of this equation provides a better characterization of the timing of reionization by smoothly linking the pre-overlap with the post-overlap phases of such a process. We confirm the validity of the quasi-instantaneous approximation as a predictor of reionization completion/maintenance and discuss new insights on the sources of cosmic reionization using the improved formalism. A constant emission rate into the intergalactic medium (IGM) of three Lyman continuum (LyC) photons per atom per gigayear leads to a reionization history that is consistent with a number of observational constraints on the ionization state of the z = 5-9 universe. While star-forming galaxies can dominate the reionization process if the luminosity-weighted fraction of LyC photons that escape into the IGM,fesc, exceeds 15% (for a faint magnitude cut-off of the galaxy UV luminosity function Mlim = -13 of and a LyC photon yield per unit 1500 å luminosity of ϵion 1025.3 erg Hz), simple models where the product of the two unknowns fesc ϵion is not evolving with redshift fail to reproduce the changing neutrality of the IGM observed at these epochs.