z ∼ 2–9 Galaxies Magnified by the Hubble Frontier Field Clusters. II. Luminosity Functions and Constraints on a Faint-end Turnover

Abstract

We present new determinations of the rest-UV luminosity functions (LFs) at z = 2–9 to extremely low luminosities (>−14 mag) from a sample of >2500 lensed galaxies found behind the Hubble Frontier Fields (HFF) clusters. For the first time, we present faint-end slope results from lensed samples that are fully consistent with blank-field results over the redshift range z = 2–9, while reaching to much lower luminosities than possible from the blank-field studies. Combining the deep lensed sample with the large blank-field samples allows us to set tight constraints on the faint-end slope α of the z = 2–9 UV LFs and its evolution. We find a smooth flattening in α from −2.28 ± 0.10 ( z = 9) to −1.53 ± 0.03 ( z = 2) with cosmic time ( dα / dz = −0.11 ± 0.01), fully consistent with dark matter halo buildup. We utilize these new results to present new measurements of the evolution in the UV luminosity density ρ UV brighter than −13 mag from z ∼ 9 to z ∼ 2. Accounting for the star formation rate (SFR) densities to faint luminosities implied by our LF results, we find that unobscured star formation dominates the SFR density at z ≳ 4, with obscured star formation dominant thereafter. Having shown we can quantify the faint-end slope α of the LF accurately with our lensed HFF samples, we also quantify the apparent curvature in the shape of the UV LF through a curvature parameter δ . The constraints on the curvature δ strongly rule out the presence of a turn-over brighter than −13.1 mag at z ∼ 3, −14.3 mag at z ∼ 6, and −15.5 mag at all other redshifts between z ∼ 9 and z ∼ 2.