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

We use the largest sample of z~6 galaxies to date from the first four Hubble Frontier Fields clusters to set constraints on the shape of the z~6 luminosity functions (LFs) to fainter than Muv=-14 mag. We quantify, for the first time, the impact of magnification uncertainties on LF results and thus provide more realistic constraints than other recent work. Our simulations reveal that for the highly-magnified sources the systematic uncertainties can become extremely large fainter than -14 mag, reaching several orders of magnitude at 95% confidence at ~-12 mag. Our new forward-modeling formalism incorporates the impact of magnification uncertainties into the LF results by exploiting the availability of many independent magnification models for the same cluster. One public magnification model is used to construct a mock high-redshift galaxy sample that is then analyzed using the other magnification models to construct a LF. Large systematic errors occur at high magnifications (mu>30) because of differences between the models. The volume densities we derive for faint (>-17 mag) sources are ~3-4x lower than one recent report and give a faint-end slope alpha=-1.92+/-0.04, which is 3.0-3.5sigma shallower (including or not including the size uncertainties, respectively). We introduce a new curvature parameter delta to model the faint end of the LF and demonstrate that the observations permit (at 68% confidence) a turn-over at z~6 in the range -15.3 to -14.2 mag, depending on the assumed lensing model. The present consideration of magnification errors and new size determinations raise doubts about previous reports regarding the form of the LF at >-14 mag. We discuss the implications of our turn-over constraints in the context of recent theoretical predictions.