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 Hubble Space Telescope Advanced Camera for Surveys imaging. The Hercules and Leo IV galaxies are extremely low luminosity (M sub(V) = -6.2,-5.5), metal-poor ([left angle bracket][Fe/H][right angle bracket] = -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 M- sub([middot in circle]), the IMF is best fit by a power-law slope of alpha = 1.2 super(+0.4) sub(-0.5) for Hercules and alpha = 1.3 + or - 0.8 for Leo IV. For Hercules, the IMF slope is more shallow than a Salpeter ( alpha = 2.35) IMF at the 5.8[sigma] level, and a Kroupa ( alpha = 2.3 above 0.5M sub([middot in circle])-) IMF slope at 5.4[sigma] level. We simultaneously fit for the binary fraction, f sub(binary), finding f sub(binary) = 0.47 super(+0.16) sub(-0.14) for Hercules, and 0.47 super(+0.37) sub(-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 0.5-0.8M sub([middot in circle])-, 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.