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Recent analysis of strongly-lensed sources in the Hubble Frontier Fieldsindicates that the rest-frame UV luminosity function of galaxies at $z=$6--8rises as a power law down to $M_\mathrm{UV}=-15$, and possibly as faint as-12.5. We use predictions from a cosmological radiation hydrodynamic simulationto map these luminosities onto physical space, constraining the minimum darkmatter halo mass and stellar mass that the Frontier Fields probe. Whilepreviously-published theoretical studies have suggested or assumed that earlystar formation was suppressed in halos less massive than $10^9$--$10^{11}M_\odot$, we find that recent observations demand vigorous star formation inhalos at least as massive as (3.1, 5.6, 10.5)$\times10^9 M_\odot$ at$z=(6,7,8)$. Likewise, we find that Frontier Fields observations probe down tostellar masses of (8.1, 18, 32)$\times10^6 M_\odot$; that is, they areobserving the likely progenitors of analogues to Local Group dwarfs such asPegasus and M32. Our simulations yield somewhat different constraints than twocomplementary models that have been invoked in similar analyses, emphasizingthe need for further observational constraints on the galaxy-halo connection.

The Minimum Halo Mass for Star Formation at z = 6 - 8