Abstract
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, 5, 6 and 7. SFR functions provide a more physical description of galaxy
build-up at high redshift and allow for direct comparisons to other techniques
for determining the SFRs at lower redshifts. The present SFR functions are
based on well-established z~4-7 UV LFs, UV-continuum slope trends with redshift
and luminosity, and IRX-beta relations, and are well-described by Schechter
relations. We extend the comparison baseline to z~2 by considering recent
determinations of the H\alpha and mid-IR luminosity functions. We find that
the high-end turnover of the SFR function, log SFR*, increases linearly with
cosmic time from ~5 M_sun/yr at z~8, 650 Myr after the Big Bang, to ~100
M_sun/yr at z~2, ~2.5 Gyr later. Recent results at z~10, close to the onset of
galaxy formation, are consistent with this trend. These results provide strong
evidence that galaxies build up uniformly over the first 3 Gyr of cosmic time.
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. The
low-end slopes of the SFR functions are flatter than for the UV LFs,
\Delta\alpha\sim+0.13, and show no clear evolution with cosmic time (z~0-7).
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