A Steep Faint-end Slope of the Uv Luminosity Function at Z ∼ 2− 3: Implications for the Global Stellar Mass Density and Star Formation in Low Mass Halos

We use the deep ground-based optical photometry of the Lyman Break Galaxy (LBG) Survey to derive robust measurements of the faint-end slope (α) of the UV luminosity function (LF) at redshifts 1.9 ≤ z ≤ 3.4. Our sample includes > 2000 spectroscopic redshifts and ≈ 31000 LBGs in 31 spatiallyindependent fields over a total area of 3261 arcmin. These data allow us to select galaxies to 0.07L and 0.10L at z ∼ 2 and z ∼ 3, respectively. A maximum-likelihood analysis indicates steep values of α(z = 2) = −1.73± 0.07 and α(z = 3) = −1.73± 0.13. This result is robust to luminosity-dependent systematics in the Lyα equivalent width and reddening distributions, is similar to the steep values advocated at z & 4, and implies that ≈ 93% of the unobscured UV luminosity density at z ∼ 2 − 3 arises from sub-L galaxies. With a realistic luminosity-dependent reddening distribution, faint to moderately luminous galaxies account for & 70% and & 25% of the bolometric luminosity density and present-day stellar mass density, respectively, when integrated over 1.9 ≤ z < 3.4. We find a factor of 8− 9 increase in the star formation rate density between z ∼ 6 and z ∼ 2, due to both a brightening of L and an increasing dust correction proceeding to lower redshifts. Combining the UV LF with stellar mass estimates suggests a relatively steep low mass slope of the stellar mass function at high redshift. The previously observed discrepancy between the integral of the star formation history and stellar mass density measurements at z ∼ 2 may be reconciled by invoking a luminosity-dependent reddening correction to the star formation history combined with an accounting for the stellar mass contributed by UV-faint galaxies. The steep and relatively constant faint-end slope of the UV LF at z & 2 contrasts with the shallower slope inferred locally, suggesting that the evolution in the faint-end slope may be dictated simply by the availability of low mass halos capable of supporting star formation at z . 2. Subject headings: galaxies: evolution — galaxies: formation — galaxies: high redshift — galaxies: luminosity function