UV luminosity functions at Redshifts z ∼ 4 TO z ∼ 10: 10,000 galaxies from HST legacy fields

The remarkable Hubble Space Telescope (HST) data sets from the CANDELS, HUDF09, HUDF12, ERS, and BoRG/HIPPIES programs have allowed us to map the evolution of the rest-frame UV luminosity function (LF) from $z\sim 10$ to $z\sim 4$. We develop new color criteria that more optimally utilize the full wavelength coverage from the optical, near-IR, and mid-IR observations over our search fields, while simultaneously minimizing the incompleteness and eliminating redshift gaps. We have identified 5859, 3001, 857, 481, 217, and 6 galaxy candidates at $z\sim 4$, $z\sim 5$, $z\sim 6$, $z\sim 7$, $z\sim 8$, and $z\sim 10$, respectively, from the ∼1000 arcmin² area covered by these data sets. This sample of >10,000 galaxy candidates at $z⩾4$ is by far the largest assembled to date with HST. The selection of $z\sim$ 4–8 candidates over the five CANDELS fields allows us to assess the cosmic variance; the largest variations are at $z⩾7$. Our new LF determinations at $z\sim 4$ and $z\sim 5$ span a 6 mag baseline and reach to –16 AB mag. These determinations agree well with previous estimates, but the larger samples and volumes probed here result in a more reliable sampling of $>L^{\ast }$ galaxies and allow us to reassess the form of the UV LFs. Our new LF results strengthen our earlier findings to $3.4\sigma$ significance for a steeper faint-end slope of the UV LF at $z>4$, with α evolving from $\alpha =-1.64\pm 0.04$ at $z\sim 4$ to $\alpha =-2.06\pm 0.13$ at $z\sim 7$ (and $\alpha =-2.02\pm 0.23$ at $z\sim 8$), consistent with that expected from the evolution of the halo mass function. We find less evolution in the characteristic magnitude M^* from $z\sim 7$ to $z\sim 4;$ the observed evolution in the LF is now largely represented by changes in ${\varphi }^{\ast }$. No evidence for a non-Schechter-like form to the z ∼ 4–8 LFs is found. A simple conditional LF model based on halo growth and evolution in the M/L ratio $(\propto {(1+z)}^{-1.5})$ of halos provides a good representation of the observed evolution.