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) fromz 10 toz 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 atz 4,z 5,z 6,z 7,z 8, andz 10, respectively, from the ∼1000 arcmin 2 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 ofz 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 atz 4 andz 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* galaxies and allow us to reassess the form of the UV LFs. Our new LF results strengthen our earlier findings to s 3.4 significance for a steeper faint-end slope of the UV LF at > z 4, with α evolving from a = - 1.64 0.04 atz 4 to a = - 2.06 0.13 atz 7 (and a = - 2.02 0.23 atz 8), consistent with that expected from the evolution of the halo mass function. We find less evolution in the characteristic magnitude M * fromz 7 toz 4; the observed evolution in the LF is now largely represented by changes in f*. 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 µ +z ( ( 1) ) 1.5 of halos provides a good representation of the observed evolution.

Ultra-deep Advanced Camera for Surveys (ACS) and WFC3/IR HUDF+HUDF09 data, along with the wide-area GOODS+ERS+CANDELS data over the CDF-S GOODS field, are used to measure UV colors, expressed as the UV-continuum slope β, of star-forming galaxies over a wide range of luminosity (0.1L * z=3 to 2L * z=3 ) at high redshift (z ∼ 7 to z ∼ 4). β is measured using all ACS and WFC3/IR passbands uncontaminated by Lyα and spectral breaks. Extensive tests show that our β measurements are only subject to minimal biases. Using a different selection procedure, Dunlop et al. recently found large biases in their β measurements. To reconcile these different results, we simulated both approaches and found that β measurements for faint sources are subject to large biases if the same passbands are used both to select the sources and to measure β. High-redshift galaxies show a well-defined restframe UV color-magnitude (CM) relationship that becomes systematically bluer toward fainter UV luminosities. No evolution is seen in the slope of the UV CM relationship in the first 1.5 Gyr, though there is a small evolution in the zero point to redder colors from z ∼ 7 to z ∼ 4. This suggests that galaxies are evolving along a well-defined sequence in the L UV -color (β) plane (a "star-forming sequence"?). Dust appears to be the principal factor driving changes in the UV color β with luminosity. These new larger β samples lead to improved dust extinction estimates at z ∼ 4-7 and confirm that the extinction is essentially zero at low luminosities and high redshifts. Inclusion of the new dust extinction results leads to (1) excellent agreement between the star formation rate (SFR) density at z ∼ 4-8 and that inferred from the stellar mass density; and (2) to higher specific star formation rates (SSFRs) at z 4, suggesting that the SSFR may evolve modestly (by factors of ∼2) from z ∼ 4-7 to z ∼ 2.

We identify 73 z ∼ 7 and 59 z ∼ 8 candidate galaxies in the reionization epoch, and use this large 26-29.4 AB mag sample of galaxies to derive very deep luminosity functions to < −18 AB mag and the star formation rate density at z ∼ 7 and z ∼ 8 (just 800 Myr and 650 Myr after recombination, respectively). The galaxy sample is derived using a sophisticated Lyman-Break technique on the full two-year WFC3/IR and ACS data available over the HUDF09 (∼29.4 AB mag, 5σ), two nearby HUDF09 fields (∼29 AB mag, 5σ, 14 arcmin 2 ) and the wider area ERS (∼27.5 AB mag, 5σ, ∼40 arcmin 2 ). The application of strict optical non-detection criteria ensures the contamination fraction is kept low (just ∼7% in the HUDF). This very low value includes a full assessment of the contamination from lower redshift sources, photometric scatter, AGN, spurious sources, low mass stars, and transients (e.g., SNe). From careful modeling of the selection volumes for each of our search fields we derive luminosity functions for galaxies at z ∼ 7 and z ∼ 8 to < −18 AB mag. The faint-end slopes α at z ∼ 7 and z ∼ 8 are uncertain but very steep at α = −2.01 ± 0.21 and α = −1.91 ± 0.32, respectively. Such steep slopes contrast to the local α ∼ −1.4 and may even be steeper than that at z ∼ 4 where α = −1.73 ± 0.05. With such steep slopes (α −1.7) lower luminosity galaxies dominate the galaxy luminosity density during the epoch of reionization. The star formation rate densities derived from these new z ∼ 7 and z ∼ 8 luminosity functions are consistent with the trends found at later times (lower redshifts). We find reasonable consistency, with the SFR densities implied from reported stellar mass densities, being only ∼40% higher at z < 7. This suggests that (1) the stellar mass densities inferred from the Spitzer IRAC photometry are reasonably accurate and (2) that the IMF at very high redshift may not be very different from that at later times. HUDF09 observationsThe full two-year WFC3/IR observations from the HUDF09 program consist of 192 orbits of ultra-deep WFC3/IR data over the HUDF09 (111 orbits), HUDF09-

We measure the UV-continuum slope β for over 4000 high-redshift galaxies over 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 β results reach very faint levels at z ∼ 4 (−15.5 mag: 0.006 L * z=3 ), z ∼ 5 (−16.5 mag: 0.014 L * z=3 ), and z ∼ 6 and z ∼ 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 β 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 data set, suffered from small systematic errors in β. We find that after correcting for the systematic errors (typically Δβ ∼ 0.1-0.2) all β results at z ∼ 7 from different groups are in excellent agreement. The mean β we measure for faint (−18 mag: 0.1 L * z=3 ) z ∼ 4, z ∼ 5, z ∼ 6, and z ∼ 7 galaxies 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 β values are redder than we have reported in the past, but bluer than other recent results. Our previously reported trend of bluer β's at lower luminosities is confirmed, as is the evolution to bluer β's at high redshifts. β appears to show only a mild luminosity dependence faintward of M UV,AB ∼ −19 mag, suggesting that the mean β asymptotes to ∼ −2.2 to −2.4 for faint z 4 galaxies. At z ∼ 7, the observed β's suggest non-zero, but low dust extinction, and they agree well with values predicted in cosmological hydrodynamical simulations.

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