We measure new estimates for the galaxy stellar mass function and star formation rates for samples of galaxies at z ∼ 4, 5, 6 & 7 using data in the CANDELS GOODS South field. The deep near-infrared observations allow us to construct the stellar mass function at z 6 directly for the first time. We estimate stellar masses for our sample by fitting the observed spectral energy distributions with synthetic stellar populations, including nebular line and continuum emission. The observed UV luminosity functions for the samples are consistent with previous observations, however we find that the observed M U V -M * relation has a shallow slope more consistent with a constant mass to light ratio and a normalisation which evolves with redshift. Our stellar mass functions have steep low-mass slopes (α ≈ −1.9), steeper than previously observed at these redshifts and closer to that of the UV luminosity function. Integrating our new mass functions, we find the observed stellar mass density evolves from log 10 ρ * = 6.64 +0.58 −0.89 at z ∼ 7 to 7.36 ± 0.06 M Mpc −3 at z ∼ 4. Finally, combining the measured UV continuum slopes (β) with their rest-frame UV luminosities, we calculate dust corrected star-formation rates (SFR) for our sample. We find the specific star-formation rate for a fixed stellar mass increases with redshift whilst the global SFR density falls rapidly over this period. Our new SFR density estimates are higher than previously observed at this redshift.

Distant star-forming galaxies show a correlation between their star formation rates (SFR) and stellar masses, and this has deep implications for galaxy formation. Here, we present a study on the evolution of the slope and scatter of the SFR-stellar mass relation for galaxies at 3.5 ≤ z ≤ 6.5 using multiwavelength photometry in GOODS-S from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) and Spitzer Extended Deep Survey. We describe an updated, Bayesian spectral-energy distribution fitting method that incorporates effects of nebular line emission, star formation histories that are constant or rising with time, and different dust attenuation prescriptions (starburst and Small Magellanic Cloud). From z=6.5 to z=3.5 star-forming galaxies in CANDELS follow a nearly unevolving correlation between stellar mass and SFR that follows SFR ∼ M a with a= 0.54 ± 0.16 at z ∼ 6 and 0.70 ± 0.21 at z ∼ 4. This evolution requires a star formation history that increases with decreasing redshift (on average, the SFRs of individual galaxies rise with time). The observed scatter in the SFR-stellar mass relation is tight, σ(log SFR/M yr −1 ) < 0.3 − 0.4 dex, for galaxies with log M /M > 9 dex. Assuming that the SFR is tied to the net gas inflow rate (SFR ∼Ṁ gas ), then the scatter in the gas inflow rate is also smaller than 0.3−0.4 dex for star-forming galaxies in these stellar mass and redshift ranges, at least when averaged over the timescale of star formation. We further show that the implied star formation history of objects selected on the basis of their co-moving number densities is consistent with the evolution in the SFR-stellar mass relation.

We present galaxy stellar mass functions (GSMFs) at z = 4-8 from a rest-frame ultraviolet (UV) selected sample of ∼4500 galaxies, found via photometric redshifts over an area of ∼280 arcmin 2 in the CANDELS/GOODS fields and the Hubble Ultra Deep Field. The deepest Spitzer/IRAC data yet-to-date and the relatively large volume allow us to place a better constraint at both the lowand high-mass ends of the GSMFs compared to previous space-based studies from pre-CANDELS observations. Supplemented by a stacking analysis, we find a linear correlation between the restframe UV absolute magnitude at 1500Å (M UV ) and logarithmic stellar mass (log M * ) that holds for galaxies with log(M * /M ) 10. We use simulations to validate our method of measuring the slope of the log M * -M UV relation, finding that the bias is minimized with a hybrid technique combining photometry of individual bright galaxies with stacked photometry for faint galaxies. The resultant measured slopes do not significantly evolve over z = 4-8, while the normalization of the trend exhibits a weak evolution toward lower masses at higher redshift. We combine the log M * -M UV distribution with observed rest-frame UV luminosity functions at each redshift to derive the GSMFs, finding that the low-mass-end slope becomes steeper with increasing redshift from α = −1.55 +0.08 −0.07 at z = 4 to α = −2.25 +0.72 −0.35 at z = 8. The inferred stellar mass density, when integrated over M * = 10 8 -10 13 M , increases by a factor of 10 +30 −2 between z = 7 and z = 4 and is in good agreement with the time integral of the cosmic star formation rate density. HST Data and Sample SelectionThe galaxy sample employed in this study is from Finkelstein et al. (2015), to which we refer the reader for full details of the HST data used and the galaxy sample selection. This sample consists of ∼7000 galaxies selected via photometric redshifts over a redshift range of z = 3.5-8.5. These galaxies were selected using HST