THE STAR FORMATION RATE FUNCTION FOR REDSHIFT z ∼ 4-7 GALAXIES: EVIDENCE FOR A UNIFORM BUILDUP OF STAR-FORMING GALAXIES DURING THE FIRST 3 Gyr OF COSMIC TIME

We combine recent estimates of dust extinction at z similar to 4-7 with UV luminosity function (LF) determinations to derive star formation rate (SFR) functions at z similar to 4-7. SFR functions provide a more physical description of galaxy buildup at high redshift and allow for direct comparisons to SFRs at lower redshifts determined by a variety of techniques. Our SFR functions are derived from well-established z similar to 4-7 UV LFs, UV-continuum slope trends with redshift and luminosity, and infrared excess (IRX)-beta relations. They are well described by Schechter relations. We extend the comparison baseline for SFR functions to z similar to 2 by considering recent determinations of the H alpha and mid-IR LFs. The low-end slopes of the SFR functions are flatter than for the UV LFs, Delta alpha similar to + 0.13, and show no clear evolution with cosmic time (z similar to 0-7). In addition, we find that the characteristic value SFR* from the Schechter fit to the SFR function exhibits consistent, and substantial, linear growth as a function of redshift from similar to 5M(circle dot) yr(-1) at z similar to 8, 650 Myr after the big bang, to similar to 100M(circle dot) yr(-1) at z similar to 2, similar to 2.5Gyr later. Recent results at z similar to 10, close to the onset of galaxy formation, are consistent with this trend. The uniformity of this evolution is even greater than seen in the UV LF over the redshift range z similar to 2-8, providing validation for our dust corrections. These results provide strong evidence that galaxies build up uniformly over the first 3 Gyr of cosmic time.