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
Smit, R., Bouwens, R. J., Franx, M., Illingworth, G. D., Labbé, I., Oesch, P. A., and van Dokkum, P. G.
We combine recent estimates of dust extinction at z ~ 4-7 with UV luminosity function (LF) determinations to derive star formation rate (SFR) functions at z ~ 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 ~ 4-7 UV LFs, UV-continuum slope trends with redshift and luminosity, and infrared excess (IRX)-β relations. They are well described by Schechter relations. We extend the comparison baseline for SFR functions to z ~ 2 by considering recent determinations of the Hα and mid-IR LFs. The low-end slopes of the SFR functions are flatter than for the UV LFs, Δα ~ +0.13, and show no clear evolution with cosmic time (z ~ 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 ~5 M &sun; yr-1 at z ~ 8, 650 Myr after the big bang, to ~100 M &sun; yr-1 at z ~ 2, ~2.5 Gyr later. Recent results at z ~ 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 ~ 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.