The Stellar Initial Mass Function of Ultra-Faint Dwarf Galaxies:
  Evidence for IMF Variations with Galactic Environment
  We present constraints on the stellar initial mass function (IMF) in two
ultra-faint dwarf (UFD) galaxies, Hercules and Leo IV, based on deep HST/ACS
imaging. The Hercules and Leo IV galaxies are extremely low luminosity (M_V =
-6.2, -5.5), metal-poor (<[Fe/H]>= -2.4, -2.5) systems that have old stellar
populations (> 11 Gyr). Because they have long relaxation times, we can
directly measure the low-mass stellar IMF by counting stars below the
main-sequence turnoff without correcting for dynamical evolution. Over the
stellar mass range probed by our data, 0.52 - 0.77 Msun, the IMF is best fit by
a power-law slope of alpha = 1.2^{+0.4}_{-0.5} for Hercules and alpha = 1.3 +/-
0.8 for Leo IV. For Hercules, the IMF slope is more shallow than a Salpeter IMF
(alpha=2.35) at the 5.8-sigma level, and a Kroupa IMF (alpha=2.3 above 0.5
Msun) at 5.4-sigma level. We simultaneously fit for the binary fraction,
finding f_binary = 0.47^{+0.16}_{-0.14} for Hercules, and 0.47^{+0.37}_{-0.17}
for Leo IV. The UFD binary fractions are consistent with that inferred for
Milky Way stars in the same mass range, despite very different metallicities.
In contrast, the IMF slopes in the UFDs are shallower than other galactic
environments. In the mass range 0.5 - 0.8 Msun, we see a trend across the
handful of galaxies with directly measured IMFs such that the power-law slopes
become shallower (more bottom-light) with decreasing galactic velocity
dispersion and metallicity. This trend is qualitatively consistent with results
in elliptical galaxies inferred via indirect methods and is direct evidence for
IMF variations with galactic environment.
