We present a robust measurement and analysis of the rest-frame ultraviolet (UV) luminosity functions at z = 4 to 8. We use deep Hubble Space Telescope imaging over the CANDELS/GOODS fields, the Hubble Ultra Deep Field and the Hubble Frontier Field deep parallel observations near the Abell 2744 and MACS J0416.1-2403 clusters. The combination of these surveys provides an effective volume of 0.6-1.2 ×10 6 Mpc 3 over this epoch, allowing us to perform a robust search for faint (M UV = −18) and bright (M UV < −21) highredshift galaxies. We select candidate galaxies using a well-tested photometric redshift technique with careful screening of contaminants, finding a sample of 7446 candidate galaxies at 3.5 < z < 8.5, with >1000 galaxies at z ≈ 6 -8. We measure both a stepwise luminosity function for candidate galaxies in our redshift samples, as well as a Schechter function, using a Markov Chain Monte Carlo analysis to measure robust uncertainties. At the faint end our UV luminosity functions agree with previous studies, yet we find a higher abundance of UV-bright candidate galaxies at z ≥ 6. Our best-fit value of the characteristic magnitude M * UV is consistent with −21 at z ≥ 5, different than that inferred based on previous trends at lower redshift, and brighter at ∼2σ significance than previous measures at z = 6 and 7 (Bouwens et al. 2007(Bouwens et al. , 2011b. At z = 8, a single powerlaw provides an equally good fit to the UV luminosity function, while at z = 6 and 7, an exponential cutoff at the bright end is moderately preferred. We compare our luminosity functions to semi-analytical models, and find that the lack of evolution in M * UV is consistent with models where the impact of dust attenuation on the bright end of the luminosity function decreases at higher redshift, though a decreasing impact of feedback may also be possible. We measure the evolution of the cosmic star-formation rate (SFR) density by integrating our observed luminosity functions to M UV = −17, correcting for dust attenuation, and find that the SFR density declines proportionally to (1+z) −4.3±0.5 at z > 4, consistent with observations at z ≥ 9. Our observed luminosity functions are consistent with a reionization history that starts at z 10, completes at z > 6, and reaches a midpoint (x HII = 0.5) at 6.7 < z < 9.4. Finally, using a constant cumulative number density selection and an empirically derived rising star-formation history, our observations predict that the abundance of bright z = 9 galaxies is likely higher than previous constraints, though consistent with recent estimates of bright z ∼ 10 galaxies.

We present the results of a numerical study comparing photometric and physical properties of simulated z= 6–9 galaxies to the observations taken by the Wide Field Camera 3 instrument aboard the Hubble Space Telescope. Using cosmological hydrodynamical simulations we find good agreement with observations in colour–colour space at all studied redshifts. We also find good agreement between observations and our Schechter luminosity function fit in the observable range, Muv≤−18, provided that a moderate dust extinction effect exists for massive galaxies. However beyond what currently can be observed, simulations predict a very large number of low‐mass galaxies and evolving steep faint‐end slopes from αL=−2.15 at z= 6 to αL=−2.64 at z= 9, with a dependence of |αL| ∝ (1 +z)0.59. During the same epoch, the normalization ϕ* increases and the characteristic magnitude becomes moderately brighter with decreasing redshift. We find similar trends for galaxy stellar mass function with evolving low‐mass end slope from αM=−2.26 at z= 6 to αM=−2.87 at z= 9, with a dependence of |αM| ∝ (1 +z)0.65. Together with our recent result on the high escape fraction of ionizing photons for low‐mass galaxies, our results suggest that the low‐mass galaxies are important contributor of ionizing photons for the reionization of the Universe at z≥ 6.

We utilize the hydrodynamic and N-body code GIZMO coupled with our newly developed sub-grid Population III (Pop III) Legacy model, designed specifically for cosmological volume simulations, to study the baseline metal enrichment from Pop III star formation at z > 7. In this idealized numerical experiment, we only consider Pop III star formation. We find that our model Pop III star formation rate density (SFRD), which peaks at ∼ 10 −3 M yr −1 Mpc −1 near z ∼ 10, agrees well with previous numerical studies and is consistent with the observed estimates for Pop II SFRDs. The mean Pop III metallicity rises smoothly from z = 25 − 7, but does not reach the critical metallicity value, Z crit = 10 −4 Z , required for the Pop III to Pop II transition in star formation mode until z 7. This suggests that, while individual halos can suppress in-situ Pop III star formation, the external enrichment is insufficient to globally terminate Pop III star formation. The maximum enrichment from Pop III star formation in star forming dark matter halos is Z ∼ 10 −2 Z , whereas the minimum found in externally enriched haloes is Z 10 −7 Z . Finally, mock observations of our simulated IGM enriched with Pop III metals produce equivalent widths similar to observations of an extremely metal poor damped Lyman alpha (DLA) system at z = 7.04, which is thought to be enriched by Pop III star formation only.

We present the results of a numerical study examining the effect of an H 2 -based star formation (SF) model on the rest-frame UV luminosity function and star formation rate function (SFRF) of z 6 galaxies, and the implications for reionization. Using cosmological hydrodynamical simulations outfitted with an H 2 -SF model, we find good agreement with our previous results (non-H 2 SF model) and observations at M uv −18. However, at M uv > −18, we find that the LF deviates from both our previous work and current observational extrapolations, producing significantly fewer low-luminosity galaxies and exhibiting additional turnover at the faint end. We constrain the redshift evolution of this turnover point using a modified Schechter function that includes additional terms to quantify the turnover magnitude (M t uv ) and subsequent slope (β). We find that M t uv evolves from M t uv = −17.33 (at z = 8) to −15.38 (z = 6), while β becomes shallower by Δβ = 0.22 during the same epoch. This occurs in an M uv range that will be observable by James Webb Space Telescope. By integrating the SFRF, we determine that even though the H 2 -SF model significantly reduces the number density of low-luminosity galaxies at M uv > −18, it does not suppress the total SFR density enough to affect the capability of SF to maintain reionization.

Some observations have shown that star formation (SF) correlates tightly with the presence of molecular hydrogen (H 2 ); therefore, it is important to investigate its implication on galaxy formation in a cosmological context. In the present work, we implement a sub-grid model (hereafter H 2 -SF model) that tracks the H 2 mass fraction within our cosmological smoothed particle hydrodynamics code GADGET-3 by using an equilibrium analytic model of Krumholz et al. This model allows us to regulate the SF in our simulation by the local abundance of H 2 rather than the total cold gas density, which naturally introduces the dependence of SF on metallicity. We investigate the implications of the H 2 -SF model on galaxy population properties, such as the stellar-to-halo mass ratio (SHMR), baryon fraction, cosmic star formation rate density (SFRD), galaxy specific SFR, galaxy stellar mass functions (GSMF), and Kennicutt-Schmidt (KS) relationship. The advantage of our work over the previous ones is having a large sample of simulated galaxies in a cosmological volume from high redshift to z = 0. We find that low-mass halos with M DM < 10 10.5 M are less efficient in producing stars in the H 2 -SF model at z 6, which brings the simulations into better agreement with the observational estimates of the SHMR and GSMF at the low-mass end. This is particularly evident by a reduction in the number of low-mass galaxies at M 10 8 M in the GSMF. The overall SFRD is also reduced at high z in the H 2 run, which results in slightly higher SFRD at low redshift due to more abundant gas available for SF at later times. This new H 2 model is able to reproduce the empirical KS relationship at z = 0 naturally, without the need for setting its normalization by hand, and overall it seems to have more advantages than the previous pressure-based SF model.