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 ( HST ) and existing ACS/WFC and WFC3/IR imaging of three lensing galaxy clusters , Abell 2744 and MACSJ0717 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 5 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 \alpha = -1.56 \pm 0.04 , \alpha = -1.72 \pm 0.04 and \alpha = -1.94 \pm 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 \sim 1.3 to z \sim 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 ( \alpha = -1.55 \pm 0.06 , -1.69 \pm 0.07 and -1.79 \pm 0.08 for z \sim 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 .