Metallicity Distribution Function of the Eridanus~II Ultra-Faint Dwarf Galaxy from Hubble Space Telescope Narrow-band Imaging.

We use deep narrowband Ca HK [Fe/H] $< -3$) that are marginally bright enough for spectroscopic follow up. Eri II's MDF appears well-described by a leaky box chemical evolution model. We also compute an updated orbital history for Eri II using Gaia eDR3 proper motions, and find that it is likely on first infall into the Milky Way. Our findings suggest that Eri II underwent an evolutionary history similar to that of an isolated galaxy. Compared to MDFs for select cosmological simulations of similar mass galaxies, we find that Eri II has a lower fraction of stars with [Fe/H] $< -3$, though such comparisons should currently be treated with caution due to a paucity of simulations, selection effects, and known limitations of Ca H&K for EMPs. This study demonstrates the power of deep HST CaHK imaging for measuring the MDFs of UFDs.