SIMBAD references

We present comprehensive analyses of faint dropout galaxies up to z ∼ 10 with the first full-depth data set of the A2744 lensing cluster and parallel fields observed by the Hubble Frontier Fields (HFF) program. We identify 54 dropouts at z ∼ 5-10 in the HFF fields and enlarge the size of the z ∼ 9 galaxy sample obtained to date. Although the number of highly magnified (µ ∼ 10) galaxies is small because of the tiny survey volume of strong lensing, our study reaches the galaxies' intrinsic luminosities comparable to the deepest-field HUDF studies. We derive UV luminosity functions with these faint dropouts, carefully evaluating by intensive simulations the combination of observational incompleteness and lensing effects in the image plane, including magnification, distortion, and multiplication of images, with the evaluation of mass model dependencies. Our results confirm that the faint-end slope, α, is as steep as -2 at z ∼ 6-8 and strengthen the evidence for the rapid decrease of UV luminosity densities, ρ_UV, at z > 8 from the large z ∼ 9 sample. We examine whether the rapid ρ_UV decrease trend can be reconciled with the large Thomson scattering optical depth, τ_e, measured by cosmic microwave background experiments, allowing a large space of free parameters, such as an average ionizing photon escape fraction and a stellar-population-dependent conversion factor. No parameter set can reproduce both the rapid ρ_UVdecrease and the large τ_e. It is possible that the ρ_UVdecrease moderates at z ≳ 11, that the free parameters significantly evolve toward high z, or that there exist additional sources of reionization such as X-ray binaries and faint active galactic nuclei.