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, {f}_{esc}, exceeds 15% (for a faint magnitude cut-off of the galaxy UV luminosity function of {M}_{lim}=-13 and a LyC photon yield per unit 1500 Å luminosity of {ξ }_{ion}={10}^25.3 {{erg}}^-1 {Hz}), simple models where the product of the two unknowns {f}_{esc}{ξ }_{ion} is not evolving with redshift fail to reproduce the changing neutrality of the IGM observed at these epochs.