intuition {#sec:intuition}
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### UV luminosity function {#sec:UVLum}

It is first constructive to illustrate how this [EoR]{} model would appear with respect to current observations. In Fig. \[fig:UVLum\], we provide a schematic picture of our single ionizing galaxy population compared to the observed non-ionizing ($\sim$ 1500 Å) UV luminosity function at $z=8$ of @Bouwens:2014p1528. To obtain the UV luminosity of our galaxy population, we use the Schechter function parameter values described in @Kuhlen:2012p1506 and abundance matching to estimate the host halo mass as a function of the UV magnitude, $M(M_{\rm UV})$. Fitting this expression as a power-law, we convert our $T^{\rm Feed}_{\rm vir}$ into a UV magnitude which produces a sharp drop in the UV luminosity function at $M_{\rm UV} = -12.6$ ($M\sim10^{8.78}\,M_{\sun}$). By construction, the non-ionizing UV luminosity function matches the observational data and we extrapolate down into the faint-end until $T^{\rm Feed}_{\rm vir}$, below which no ionizing photons are produced/escape the galaxy. In our illustrative model, this drop, tracing fundamental galaxy formation physics, is well beyond the sensitivity limits even for JWST [e.g. @Salvaterra:2011p2908], showcasing the power of our approach.

The UV luminosity function with an appropriate dust model can constrain the star formation rate, which (approximately) collapses 