We measure the UV-continuum slope \beta for over 4000 high-redshift galaxies over a wide range of redshifts z \sim 4 -8 and luminosities from the HST HUDF/XDF , HUDF09-1 , HUDF09-2 , ERS , CANDELS-N , and CANDELS-S data sets .
Our new \beta results reach very faint levels at z \sim 4 ( - 15.5 mag : 0.006 L _ { z = 3 } ^ { * } ) , z \sim 5 ( - 16.5 mag : 0.014 L _ { z = 3 } ^ { * } ) , and z \sim 6 and z \sim 7 ( - 17 mag : 0.025 L _ { z = 3 } ^ { * } ) .
Inconsistencies between previous studies led us to conduct a comprehensive review of systematic errors and develop a new technique for measuring \beta that is robust against biases that arise from the impact of noise .
We demonstrate , by object-by-object comparisons , that all previous studies , including our own and those done on the latest HUDF12 dataset , suffered from small systematic errors in \beta .
We find that after correcting for the systematic errors ( typically \Delta \beta \sim 0.1 -0.2 ) all \beta results at z \sim 7 from different groups are in excellent agreement .
The mean \beta we measure for faint ( - 18 mag : 0.1 L _ { z = 3 } ^ { * } ) z \sim 4 , z \sim 5 , z \sim 6 , and z \sim 7 galaxies is - 2.03 \pm 0.03 \pm 0.06 ( random and systematic errors ) , - 2.14 \pm 0.06 \pm 0.06 , - 2.24 \pm 0.11 \pm 0.08 , and - 2.30 \pm 0.18 \pm 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 bluer \beta ’ s at lower luminosities is confirmed , as is the evolution to bluer \beta ’ s at high redshifts . \beta appears to show only a mild luminosity dependence faintward of M _ { UV,AB } \sim - 19 mag , suggesting that the mean \beta asymptotes to \sim - 2.2 to - 2.4 for faint z \geq 4 galaxies .
At z \sim 7 , the observed \beta ’ s suggest non-zero , but low dust extinction , and they agree well with values predicted in cosmological hydrodynamical simulations .