Inferred H{\alpha} Flux as a Star-Formation Rate Indicator at z ~ 4-5:
  Implications for Dust Properties, Burstiness, and the z = 4-8
  Star-Formation-Rate Functions
  We derive H{\alpha} fluxes for a large spectroscopic and
photometric-redshift-selected sample of sources over GOODS-North and South in
the redshift range z = 3.8-5.0 with deep HST, Spitzer/IRAC, and ground-based
observations. The H{\alpha} flux is inferred based on the offset between the
IRAC 3.6 {\mu}m flux and that predicted from the best-fit SED. We demonstrate
that the H{\alpha} flux correlates well with dust- corrected UV star-formation
rate (SFR) and therefore can serve as an independent SFR indicator. However, we
also find a systematic offset in the SFR_H{\alpha}/SFR_UV ratios for z ~ 4-5
galaxies relative to local relations (assuming the same dust corrections for
nebular regions and stellar light). We show that we can resolve the modest
tension in the inferred SFRs by assuming bluer intrinsic UV slopes (increasing
the dust correction), a rising star-formation history or assuming a low
metallicity stellar population with a hard ionizing spectrum (increasing the
L_H{\alpha}/SFR ratio). Using H{\alpha} as a SFR indicator, we find a
normalization of the star formation main sequence in good agreement with recent
SED-based determinations and also derive the SFR functions at z ~ 4-8. In
addition, we assess for the first time the burstiness of star formation in z ~
4 galaxies on <100 Myr time scales by comparing UV and H{\alpha}-based sSFRs;
their one-to-one relationship argues against significantly bursty
star-formation histories. Further progress will be made on these results, by
incorporating new results from ALMA to constrain the dust-obscured star
formation in high-redshift UV-selected samples.
