Evolution of Galaxy Stellar Mass Functions, Mass Densities, and Mass-to-light Ratios from z ~ 7 to z ~ 4

Abstract

We derive stellar masses from spectral energy distribution fitting to rest-frame optical and UV fluxes for 401 star-forming galaxies at z ~ 4, 5, and 6 from Hubble-WFC3/IR camera observations of the Early Release Science field combined with the deep GOODS-S Spitzer/IRAC data (and include a previously published z ~ 7 sample). A mass-luminosity relation with strongly luminosity-dependent {M}/L_UV ratios is found for the largest sample (299 galaxies) at z ~ 4. The relation {M}\propto L_{UV,1500}^{1.7({+/- }0.2)} has a well-determined intrinsic sample variance of 0.5 dex. This relation is also consistent with the more limited samples at z ~ 5-7. This z ~ 4 mass-luminosity relation, and the well-established faint UV-luminosity functions at z ~ 4-7, are used to derive galaxy mass functions (MFs) to masses {M}\sim 10^{8} at z ~ 4-7. A bootstrap approach is used to derive the MFs to account for the large scatter in the {M}{--}L_UV relation and the luminosity function uncertainties, along with an analytical cross-check. The MFs are also corrected for the effects of incompleteness. The incompleteness-corrected MFs are steeper than previously found, with slopes α _M ~ -1.4 to -1.6 at low masses. These slopes are, however, still substantially flatter than the MFs obtained from recent hydrodynamical simulations. We use these MFs to estimate the stellar mass density (SMD) of the universe to a fixed M _{UV, AB} < - 18 as a function of redshift and find an SMD growth vprop(1 + z)^{-3.4 ± 0.8} from z ~ 7 to z ~ 4. We also derive the SMD from the completeness-corrected MFs to a mass limit {M}\sim 10^{8} M _sun. Such completeness-corrected MFs and the derived SMDs will be particularly important for comparisons as future MFs reach to lower masses.