Direct Numerical Simulation of Reionization II: Recombinations, Clumping
  Factors, and the Photon Budget for Reionization
  In this first of several application papers, we investigate the mechanics of
reionization from stellar sources in high-z galaxies, the utility of various
clumping factors on estimating the recombination time in the IGM, and the
photon budget required to achieve reionization. We test the accuracy of the
static and time-dependent models of Madau et al. as predictors of reionization
completion/maintenance. We simulate a WMAP7 LCDM cosmological model in a 20 Mpc
comoving cube with 800^3 uniform fluid cells and dark matter particles. By
tuning our star formation to approximately match the observed star formation
rate density and luminosity function, we created a fully coupled
radiation-hydro realization of H reionization which begins to ionize at z~10
and completes at z~5.8. We find that roughly 2 ionizing photons per H atom are
required to convert the neutral IGM to a highly ionized state, which supports
the "photon starved" scenario discussed by Bolton & Haehnelt. The events during
reionization that lead to this number can generally be described as inside-out,
but in reality the narrative depends on the level of ionization of the gas one
attributes to as ionized. We find that the formula for the UV photon production
rate dN/dt_ion(z) needed to maintain the IGM in an ionized state derived by
Madau et al. should not be used to predict the epoch of reionization completion
because it ignores history-dependent terms in the global ionization balance
which are not ignorable. We find that the time-dependent model for the ionized
volume fraction Q_HII is more predictive, but overestimates the redshift of
reionization completion by delta_z~1. We propose a revised formulation of the
time-dependent model which agrees with our simulation to O(1%). Finally, we use
our simulation to estimate a global UV escape fraction due to circumgalactic
gas resolved on our mesh to be <f_esc>~0.7.
