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We search the complete Hubble Frontier Field dataset of Abell 2744 and itsparallel field for z~10 sources to further refine the evolution of the cosmicstar-formation rate density (SFRD) at z>8. We independently confirm two imagesof the recently discovered triply-imaged z~9.8 source by Zitrin et al. (2014)and set an upper limit for similar z~10 galaxies with red colors ofJ_125-H_160>1.2 in the parallel field of Abell 2744. We utilize extensivesimulations to derive the effective selection volume of Lyman-break galaxies atz~10, both in the lensed cluster field and in the adjacent parallel field.Particular care is taken to include position-dependent lensing shear toaccurately account for the expected sizes and morphologies of highly-magnifiedsources. We show that both source blending and shear reduce the completeness ata given observed magnitude in the cluster, particularly near the criticalcurves. These effects have a significant, but largely overlooked, impact on thedetectability of high-redshift sources behind clusters, and substantiallyreduce the expected number of highly-magnified sources. The detections andlimits from both pointings result in a SFRD which is higher by 0.4+-0.4 dexthan previous estimates at z~10 from blank fields. Nevertheless, thecombination of these new results with all other estimates remain consistentwith a rapidly declining SFRD in the 170 Myr from z~8 to z~10 as predicted bycosmological simulations and dark-matter halo evolution in LambdaCDM. Oncebiases introduced by magnification-dependent completeness are accounted for,the full six cluster and parallel Frontier Field program will be an extremelypowerful new dataset to probe the evolution of the galaxy population at z>8before the advent of the JWST.

astrophysical journal/the astrophysical journal

First Frontier Field Constraints on the Cosmic Star-Formation Rate  Density at z~10 - The Impact of Lensing Shear on Completeness of  High-Redshift Galaxy Samples