We present a robust measurement of the rest-frame UV luminosity function (LF) and its evolution during the peak epoch of cosmic star formation at 1 z 3. We use our deep near-ultraviolet imaging from WFC3/UVIS on the Hubble Space Telescope and existing Advanced Camera for Surveys (ACS)/WFC and WFC3/IR imaging of three lensing galaxy clusters, Abell 2744 and MACS J0717 from the Hubble Frontier Field survey and Abell 1689. Combining deep UV imaging and high magnification from strong gravitational lensing, we use photometric redshifts to identify 780 ultra-faint galaxies with {M}_{UV} -12.5 AB mag at 1 z 3. From these samples, we identified five new, faint, multiply imaged systems in A1689. We run a Monte Carlo simulation to estimate the completeness correction and effective volume for each cluster using the latest published lensing models. We compute the rest-frame UV LF and find the best-fit faint-end slopes of α =-1.56+/- 0.04, α =-1.72+/- 0.04, and α =-1.94+/- 0.06 at 1.0 z 1.6, 1.6 z 2.2, and 2.2 z 3.0, respectively. Our results demonstrate that the UV LF becomes steeper from z∼ 1.3 to z∼ 2.6 with no sign of a turnover down to {M}_{UV}=-14 AB mag. We further derive the UV LFs using the Lyman break “dropout” selection and confirm the robustness of our conclusions against different selection methodologies. Because the sample sizes are so large and extend to such faint luminosities, the statistical uncertainties are quite small, and systematic uncertainties (due to the assumed size distribution, for example) likely dominate. If we restrict our analysis to galaxies and volumes above 50 % completeness in order to minimize these systematics, we still find that the faint-end slope is steep and getting steeper with redshift, though with slightly shallower (less negative) values (α =-1.55+/- 0.06, -1.69 ± 0.07, and -1.79 ± 0.08 for z∼ 1.3, 1.9, and 2.6, respectively). Finally, we conclude that the faint star-forming galaxies with UV magnitudes of -18.5 {M}_{UV} -12.5 covered in this study produce the majority (55%-60%) of the unobscured UV luminosity density at 1 z 3.

Some of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation.