The Minimum Halo Mass for Star Formation at z = 6 - 8
  Recent analysis of strongly-lensed sources in the Hubble Frontier Fields
indicates that the rest-frame UV luminosity function of galaxies at $z=$6--8
rises 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 simulation
to map these luminosities onto physical space, constraining the minimum dark
matter halo mass and stellar mass that the Frontier Fields probe. While
previously-published theoretical studies have suggested or assumed that early
star formation was suppressed in halos less massive than $10^9$--$10^{11}
M_\odot$, we find that recent observations demand vigorous star formation in
halos 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 to
stellar masses of (8.1, 18, 32)$\times10^6 M_\odot$; that is, they are
observing the likely progenitors of analogues to Local Group dwarfs such as
Pegasus and M32. Our simulations yield somewhat different constraints than two
complementary models that have been invoked in similar analyses, emphasizing
the need for further observational constraints on the galaxy-halo connection.
