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We combine recent estimates of dust extinction at z~4-7 with UV luminosityfunction (LF) determinations to derive star formation rate (SFR) functions atz~4, 5, 6 and 7. SFR functions provide a more physical description of galaxybuild-up at high redshift and allow for direct comparisons to SFRs at lowerredshifts determined by a variety of techniques. Our SFR functions are derivedfrom well-established z~4-7 UV LFs, UV-continuum slope trends with redshift andluminosity, and IRX-beta relations. They are well-described by Schechterrelations. We extend the comparison baseline for SFR functions to z~2 byconsidering recent determinations of the H{\alpha} and mid-IR luminosityfunctions. The low-end slopes of the SFR functions are flatter than for the UVLFs, \Delta\alpha\sim+0.13, and show no clear evolution with cosmic time(z~0-7). In addition, we find that the characteristic value SFR* from theSchechter fit to SFR function exhibits consistent, and substantial, lineargrowth as a function of redshift from ~5 M_sun/yr at z~8, 650 Myr after the BigBang, to ~100 M_sun/yr at z~2, ~2.5 Gyr later. Recent results at z~10, close tothe onset of galaxy formation, are consistent with this trend. The uniformityof this evolution is even greater than seen in the UV LF over the redshiftrange z~2-8, providing validation for our dust corrections. These resultsprovide strong evidence that galaxies build up uniformly over the first 3 Gyrof cosmic time.

astrophysical journal/the astrophysical journal

The Star Formation Rate Function for Redshift z~4-7 Galaxies: Evidence  for a Uniform Build-Up of Star-Forming Galaxies During the First 3 Gyr of  Cosmic Time