Critical Star-Formation Rates for Reionization: Full Reionization occurs
  at z = 7
  We assess the probable redshift (z_rei ~ 7) for full reionization of the
intergalactic medium (IGM) using a prescription for the co-moving
star-formation-rate (SFR) density (rho_SFR) required to maintain
photoionization against recombination. Our newly developed on-line 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 LyC escape fraction. The decline in
high-redshift galaxy candidates and Lya 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 rho_SFR = (0.018 M_sun/yr/Mpc^3)
[(1+z)/8]^3 (C_H/3)(0.2/f_esc) T_4^(-0.845) scaled to fiducial values of
clumping factor C_H = 3, escape fraction f_esc = 0.2, electron temperature T_e
= 10^4 K, and low-metallicity initial mass functions (IMF) and stellar
atmospheres. Our hydrodynamical + N-body simulations find a mean clumping
factor C_H = (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 f_esc at high z.
The CMB optical depth, tau_e = 0.088 +/- 0.015, can be explained by full
reionization, producing tau_e = 0.050 back to z_rei = 7, augmented by
Delta-tau_e = 0.01-0.04 in a UV/X-ray 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 Delta z ~ 3 from z =
7.5-10.5.
