CRITICAL STAR FORMATION RATES FOR REIONIZATION: FULL REIONIZATION OCCURS AT REDSHIFT z ≈ 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 (ρ-dotSFR) 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 ρ-dotSFR∼(.018 Msunyr-1Mpc-3)[(1+z)/8]3(CH/3)(0.2/fesc)T4-0.845 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.