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We measure the UV-continuum slope beta for over 4000 high-redshift galaxiesover a wide range of redshifts z~4-8 and luminosities from the HST HUDF/XDF,HUDF09-1, HUDF09-2, ERS, CANDELS-N, and CANDELS-S data sets. Our new betaresults reach very faint levels at z~4 (-15.5 mag: 0.006 L*(z=3)), z~5 (-16.5mag: 0.014L*(z=3)), and z~6 and z~7 (-17 mag: 0.025 L*(z=3)). Inconsistenciesbetween previous studies led us to conduct a comprehensive review of systematicerrors and develop a new technique for measuring beta that is robust againstbiases that arise from the impact of noise. We demonstrate, by object-by-objectcomparisons, that all previous studies, including our own and those done on thelatest HUDF12 dataset, suffer from small systematic errors in beta. We findthat after correcting for the systematic errors (typically d(beta) ~0.1-0.2)all beta results at z~7 from different groups are in excellent agreement. Themean beta we measure for faint (-18 mag: 0.1L*(z=3)) z~4, z~5, z~6, and z~7galaxies is -2.03+/-0.03+/-0.06 (random and systematic errors),-2.14+/-0.06+/-0.06, -2.24+/-0.11+/-0.08, and -2.30+/-0.18+/-0.13,respectively. Our new beta values are redder than we have reported in the past,but bluer than other recent results. Our previously reported trend of bluerbeta's at lower luminosities is confirmed, as is the evolution to bluer beta'sat high redshifts. beta appears to show only a mild luminosity dependencefaintward of M(UV,AB) ~ -19 mag, suggesting that the mean beta asymptotes to ~-2.2 to -2.4 for faint z>~4 galaxies. At z~7, the observed beta's suggestnon-zero, but low dust extinction, and they agree well with values predicted incosmological hydrodynamical simulations.

UV-Continuum Slopes of >4000 z~4-8 Galaxies from the HUDF/XDF, HUDF09, ERS, CANDELS-South, and CANDELS-North Fields