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We present novel constraints on the underlying galaxy formation physics(e.g., mass loading factor, star formation history, metal retention) at$z\gtrsim7$ for the low-mass ($M_*\sim10^5$ M$_\odot$) Local Group ultra-faintdwarf galaxy (UFD) Eridanus {\sc II} (Eri II). Using a hierarchical Bayesianframework, we apply a one-zone chemical evolution model to Eri II's CaHK-basedphotometric metallicity distribution function (MDF; [Fe/H]) and find that theevolution of Eri II is well-characterized by a short, exponentially decliningstar-formation history ($\tau_\text{SFH}=0.39\pm_{0.13}^{0.18}$ Gyr), a lowstar-formation efficiency ($\tau_\text{SFE}=27.56\pm_{12.92}^{25.14}$ Gyr), anda large mass-loading factor ($\eta=194.53\pm_{42.67}^{33.37}$). Our results areconsistent with Eri II forming the majority of its stars before the end ofreionization. The large mass-loading factor implies strong outflows in theearly history of Eri II and is in good agreement with theoretical predictionsfor the mass-scaling of galactic winds. It also results in the ejection of$>$90\% of the metals produced in Eri II. We make predictions for thedistribution of [Mg/Fe]-[Fe/H] in Eri II as well as the prevalence of ultrametal-poor stars, both of which can be tested by future chemical abundancemeasurements. Spectroscopic follow-up of the highest metallicity stars in EriII ($\text{[Fe/H]} > -2$) will greatly improve model constraints. Our newframework can readily be applied to all UFDs throughout the Local Group,providing new insights into the underlying physics governing the evolution ofthe faintest galaxies in the reionization era.

Strong Outflows and Inefficient Star Formation in the Reionization-era Ultra-faint Dwarf Galaxy Eridanus II