CRITICAL STAR FORMATION RATES FOR REIONIZATION: FULL REIONIZATION OCCURS AT REDSHIFTz≈ 7

We assess the probable redshift (zrei ≈ 7) for full reionization of the intergalactic medium (IGM) using a prescription for the comoving star formation rate (SFR) density () required to maintain photoionization against recombination. Our newly developed online reionization simulator allows users to assess the required SFR and ionization histories, using a variety of assumptions for galactic and stellar populations, IGM clumping factor and temperature, and Lyman continuum (LyC) escape fraction. The decline in high-redshift galaxy candidates and Lyα emitters at z = 6–8 suggests a rising neutral fraction, with reionization at z ≳ 7 increasingly difficult owing to increased recombination rates and constraints from the ionizing background and LyC mean free path. The required rate is scaled to fiducial values of clumping factor CH = 3, escape fraction fesc = 0.2, electron temperature Te = 104 K, and low-metallicity initial mass functions (IMFs) and stellar atmospheres. Our hydrodynamical + N-body simulations find a mean clumping factor CH ≈ (2.9)(1 + z)/6−1.1 in the photoionized, photoheated filaments at z = 5–9. The critical SFR could be reduced by increasing the minimum stellar mass, invoking a top-heavy IMF, or systematically increasing fesc at high z. The cosmic microwave background optical depth, τe = 0.088 ± 0.015, could be explained by full reionization, producing τe = 0.050 back to zrei ≈ 7, augmented by Δτe ≈ 0.01–0.04 in a partially ionized IGM at z > 7. In this scenario, the strongest 21 cm signal should occur at redshifted frequencies 124–167 MHz owing to IGM heating over an interval Δz ≈ 3 in the range z ≈ 7.5–10.5.