= Photon-budget reionization threshold
{title2=$f_{\rm coll}=N_{\rm req}/N_\gamma$}
If each collapsed baryon supplies $N_\gamma$ effective ionizing photons and $N_{\rm req}$ photons per cosmic baryon are required, the threshold collapsed fraction is $f_{\rm coll}=N_{\rm req}/N_\gamma$. The <Press-Schechter formalism> gives $\operatorname{erfc}[\delta_{\rm sc}/(\sqrt2\sigma(M_{\min},z))]=f_{\rm coll}$. Escape losses and recombinations must either be incorporated in the effective yield/requirement or counted separately, not twice.
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