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One of the most important parameters in characterizing the Epoch ofReionization, the escape fraction of ionizing photons, $f_\mathrm{esc}$,remains unconstrained both observationally and theoretically. With recent workhighlighting the impact of galaxy-scale feedback on the instantaneous value of$f_\mathrm{esc}$, it is important to develop a model in which reionization isself-consistently coupled to galaxy evolution. In this work, we present such amodel and explore how physically motivated functional forms of $f_\mathrm{esc}$affect the evolution of ionized hydrogen within the intergalactic medium. Usingthe $21$cm power spectrum evolution, we investigate the likelihood ofobservationally distinguishing between a constant $f_\mathrm{esc}$ and othermodels that depend upon different forms of galaxy feedback. We find thatchanging the underlying connection between $f_\mathrm{esc}$ and galaxy feedbackdrastically alters the large-scale $21$cm power. The upcoming Square KilometreArray Low Frequency instrument possesses the sensitivity to differentiatebetween our models at a fixed optical depth, requiring only $200$ hours ofintegration time focused on redshifts $z = 7.5-8.5$. Generalizing these resultsto account for a varying optical depth will require multiple $800$ hourobservations spanning redshifts $z = 7-10$. This presents an excitingopportunity to observationally constrain one of the most elusive parametersduring the Epoch of Reionization.

The Escape Fraction of Ionizing Photons During the Epoch of Reionization: observability with the Square Kilometre Array