The z~6 Luminosity Function Fainter than -15 mag from the Hubble Frontier Fields: The Impact of Magnification Uncertainties

The Hubble Frontier Fields (HFF) program has substantial potential for constraining both the properties and prevalence of faint galaxies in the early universe. Yet the accuracy of results derived in high magnification regions using lensing clusters is limited due to systematics. We present a new forward-modeling formalism to incorporate the impact of magnification uncertainties into luminosity function results, by exploiting the availability of many independent magnification models for the same clusters. One public lensing model is treated as the truth and used to construct a mock set of lensed high-redshift galaxies, which can then be analyzed using another magnification model (typically a median model) to construct a luminosity function. Using the most comprehensive and faintest selection of lensed z~6 galaxies to date (drawn from the first 4 HFF clusters), we derive direct constraints on the shape of the UV LF to -13.5 mag and with much greater uncertainties to -12.5 mag. Our simulations reveal that for highly-magnified sources (>~30x) the systematic uncertainties become very large, reaching several orders of magnitude at 95% confidence at ~-12 mag. The volume densities we derive for faint (>-17 mag) sources are ~3-4x lower than one recent report, with a faint-end slope -1.92+/-0.04 (3.5-sigma shallower). Introducing a new curvature parameter to model the faint end of the LF, we demonstrate that current observations permit (within the 68% confidence intervals) a turn-over in the z~6 UV LF as bright as -15.3 and -14.2 mag, respectively, if differences between the full and parameterized set of lensing models in the HFF effort are representative. We discuss the implications of such a turn over in the context of recent theoretical predictions.