We present a robust method to constrain average galaxy star formation rates, star formation histories, and the intracluster light as a function of halo mass. Our results are consistent with observed galaxy stellar mass functions, specific star formation rates, and cosmic star formation rates from z = 0 to z = 8. We consider the effects of a wide range of uncertainties on our results, including those affecting stellar masses, star formation rates, and the halo mass function at the heart of our analysis. As they are relevant to our method, we also present new calibrations of the dark matter halo mass function, halo mass accretion histories, and halo-subhalo merger rates out to z = 8. We also provide new compilations of cosmic and specific star formation rates; more recent measurements are now consistent with the buildup of the cosmic stellar mass density at all redshifts. Implications of our work include: halos near 10 12 M ⊙ are the most efficient at forming stars at all redshifts, the baryon conversion efficiency of massive halos drops markedly after z ∼ 2.5 (consistent with theories of cold-mode accretion), the ICL for massive galaxies is expected to be significant out to at least z ∼ 1 − 1.5, and dwarf galaxies at low redshifts have higher stellar mass to halo mass ratios than previous expectations and form later than in most theoretical models. Finally, we provide new fitting formulae for star formation histories that are more accurate than the standard declining tau model. Our approach places a wide variety of observations relating to the star formation history of galaxies into a self-consistent framework based on the modern understanding of structure formation in ΛCDM. Constraints on the stellar mass-halo mass relationship and star formation rates are available for download online.

We conduct a comprehensive analysis of the relationship between central galaxies and their host dark matter halos, as characterized by the stellar mass -halo mass (SM-HM) relation, with rigorous consideration of uncertainties. Our analysis focuses on results from the abundance matching technique, which assumes that every dark matter halo or subhalo above a specific mass threshold hosts one galaxy. We provide a robust estimate of the SM-HM relation for 0 < z < 1 and discuss the quantitative effects of uncertainties in observed galaxy stellar mass functions (GSMFs) (including stellar mass estimates and counting uncertainties), halo mass functions (including cosmology and uncertainties from substructure), and the abundance matching technique used to link galaxies to halos (including scatter in this connection). Our analysis results in a robust estimate of the SM-HM relation and its evolution from z=0 to z=4. The shape and evolution are well constrained for z < 1. The largest uncertainties at these redshifts are due to stellar mass estimates (0.25 dex uncertainty in normalization); however, failure to account for scatter in stellar masses at fixed halo mass can lead to errors of similar magnitude in the SM-HM relation for central galaxies in massive halos. We also investigate the SM-HM relation to z = 4, although the shape of the relation at higher redshifts remains fairly unconstrained when uncertainties are taken into account. We find that the integrated star formation at a given halo mass peaks at 10-20% of available baryons for all redshifts from 0 to 4. This peak occurs at a halo mass of 7 × 10 11 M ⊙ at z = 0 and this mass increases by a factor of 5 to z = 4. At lower and higher masses, star formation is substantially less efficient, with stellar mass scaling as M * ∼ M 2.3 h at low masses and M * ∼ M 0.29 h at high masses. The typical stellar mass for halos with mass less than 10 12 M ⊙ has increased by 0.3 − 0.45 dex for halos since z ∼ 1. These results will provide a powerful tool to inform galaxy evolution models.

We present a new algorithm for identifying dark matter halos, substructure, and tidal features. The approach is based on adaptive hierarchical refinement of friends-of-friends groups in six phase-space dimensions and one time dimension, which allows for robust (grid-independent, shape-independent, and noise-resilient) tracking of substructure; as such, it is named ROCKSTAR (Robust Overdensity Calculation using K-Space Topologically Adaptive Refinement). Our method is massively parallel (up to 10 5 CPUs) and runs on the largest current simulations (>10 10 particles) with high efficiency (10 CPU hours and 60 gigabytes of memory required per billion particles analyzed). A previous paper (Knebe et al. 2011) has shown ROCKSTAR to have excellent recovery of halo properties; we expand on these comparisons with more tests and higher-resolution simulations. We show a significant improvement in substructure recovery compared to several other halo finders and discuss the theoretical and practical limits of simulations in this regard. Finally, we present results which demonstrate conclusively that dark matter halo cores are not at rest relative to the halo bulk or substructure average velocities and have coherent velocity offsets across a wide range of halo masses and redshifts. For massive clusters, these offsets can be up to 350 km s −1 at z = 0 and even higher at high redshifts. Our implementation is publicly available at

We present a method to flexibly and self-consistently determine individual galaxies' star formation rates (SFRs) from their host haloes' potential well depths, assembly histories, and redshifts. The method is constrained by galaxies' observed stellar mass functions, SFRs (specific and cosmic), quenched fractions, UV luminosity functions, UV-stellar mass relations, autocorrelation functions (including quenched and star-forming subsamples), and quenching dependence on environment; each observable is reproduced over the full redshift range available, up to 0 < z < 10. Key findings include: galaxy assembly correlates strongly with halo assembly; quenching at z > 1 correlates strongly with halo mass; quenched fractions at fixed halo mass decrease with increasing redshift; massive quenched galaxies reside in higher-mass haloes than star-forming galaxies at fixed galaxy mass; star-forming and quenched galaxies' star formation histories at fixed mass differ most at z < 0.5; satellites have large scatter in quenching timescales after infall, and have modestly higher quenched fractions than central galaxies; Planck cosmologies result in up to 0.3 dex lower stellar-halo mass ratios at early times; and, nonetheless, stellar mass-halo mass ratios rise at z > 5. Also presented are revised stellar mass-halo mass relations for all, quenched, star-forming, central, and satellite galaxies; the dependence of star formation histories on halo mass, stellar mass, and galaxy SSFR; quenched fractions and quenching timescale distributions for satellites; and predictions for higher-redshift galaxy correlation functions and weak lensing surface densities. The public data release includes the massively parallel (> 10 5 cores) implementation (the UNI-VERSEMACHINE), the newly compiled and remeasured observational data, derived galaxy formation constraints, and mock catalogs including lightcones.

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.