Abstract
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 LF. Leveraging
this formalism against 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 (4-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
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