Inferred Hα 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 Hα 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 Hubble Space Telescope (HST), Spitzer/IRAC, and ground-based observations. The Hα flux is inferred based on the offset between the IRAC 3.6 μm flux and that predicted from the best-fit spectral energy distribution (SED). We demonstrate that the Hα 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 ${SFR}_{H\alpha }/{SFR}_{UV+\beta }$ 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 Hα as an 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 $z\sim 4\text{--}8$. In addition, we assess for the first time the burstiness of star formation in $z\sim 4$ galaxies on <100 Myr timescales by comparing UV and Hα-based sSFRs; their one-to-one relationship argues against significantly bursty star formation histories.