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Peter Behroozi

Publications and source records attributed to Peter Behroozi.

At least 109 records · Page 6Linked to original sources

Clustering Constraints on the Relative Sizes of Central and Satellite Galaxies

We empirically constrain how galaxy size relates to halo virial radius using new measurements of the size- and stellar mass-dependent clustering of galaxies in the Sloan Digital Sky Survey. We find that small galaxies cluster much more strongly than large galaxies of the same stellar mass. The magnitude of this clustering difference increases on small scales, and decreases with increasing stellar mass. Using Halotools to forward model the observations, we test an empirical model in which present-day galaxy size is proportional to the size of the virial radius at the time the halo reached its maximum mass. This simple model reproduces the observed size-dependence of galaxy clustering in striking detail. The success of this model provides strong support for the conclusion that satellite galaxies have smaller sizes relative to central galaxies of the same halo mass. Our findings indicate that satellite size is set prior to the time of infall, and that a remarkably simple, linear size--virial radius relation emerges from the complex physics regulating galaxy size. We make quantitative predictions for future measurements of galaxy-galaxy lensing, including dependence upon size, scale, and stellar mass, and provide a scaling relation of the ratio of mean sizes of satellites and central galaxies as a function of their halo mass that can be used to calibrate hydrodynamical simulations and semi-analytic models.

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MultiDark-Galaxies: data release and first results

We present the public release of the MultiDark-Galaxies: three distinct galaxy catalogues derived from one of the Planck cosmology MultiDark simulations (i.e. MDPL2, with a volume of (1 Gpc/$h$)$^{3}$ and mass resolution of $1.5 \times 10^{9} M_{\odot}/h$) by applying the semi-analytic models GALACTICUS, SAG, and SAGE to it. We compare the three models and their conformity with observational data for a selection of fundamental properties of galaxies like stellar mass function, star formation rate, cold gas fractions, and metallicities - noting that they sometimes perform differently reflecting model designs and calibrations. We have further selected galaxy subsamples of the catalogues by number densities in stellar mass, cold gas mass, and star formation rate in order to study the clustering statistics of galaxies. We show that despite different treatment of orphan galaxies, i.e. galaxies that lost their dark-matter host halo due to the finite mass resolution of the N-body simulation or tidal stripping, the clustering signal is comparable, and reproduces the observations in all three models - in particular when selecting samples based upon stellar mass. Our catalogues provide a powerful tool to study galaxy formation within a volume comparable to those probed by on-going and future photometric and redshift surveys. All model data consisting of a range of galaxy properties - including broad-band SDSS magnitudes - are publicly available.

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Forward Modeling of Large-Scale Structure: An open-source approach with Halotools

We present the first stable release of Halotools (v0.2), a community-driven Python package designed to build and test models of the galaxy-halo connection. Halotools provides a modular platform for creating mock universes of galaxies starting from a catalog of dark matter halos obtained from a cosmological simulation. The package supports many of the common forms used to describe galaxy-halo models: the halo occupation distribution (HOD), the conditional luminosity function (CLF), abundance matching, and alternatives to these models that include effects such as environmental quenching or variable galaxy assembly bias. Satellite galaxies can be modeled to live in subhalos, or to follow custom number density profiles within their halos, including spatial and/or velocity bias with respect to the dark matter profile. The package has an optimized toolkit to make mock observations on a synthetic galaxy population, including galaxy clustering, galaxy-galaxy lensing, galaxy group identification, RSD multipoles, void statistics, pairwise velocities and others, allowing direct comparison to observations. Halotools is object-oriented, enabling complex models to be built from a set of simple, interchangeable components, including those of your own creation. Halotools has an automated testing suite and is exhaustively documented on http://halotools.readthedocs.io, which includes quickstart guides, source code notes and a large collection of tutorials. The documentation is effectively an online textbook on how to build and study empirical models of galaxy formation with Python.

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GOLDRUSH. II. Clustering of Galaxies at $z\sim 4-6$ Revealed with the Half-Million Dropouts Over the 100 deg$^2$ Area Corresponding to 1 Gpc$^3$

We present clustering properties from 579,492 Lyman break galaxies (LBGs) at z~4-6 over the 100 deg^2 sky (corresponding to a 1.4 Gpc^3 volume) identified in early data of the Hyper Suprime-Cam (HSC) Subaru strategic program survey. We derive angular correlation functions (ACFs) of the HSC LBGs with unprecedentedly high statistical accuracies at z~4-6, and compare them with the halo occupation distribution (HOD) models. We clearly identify significant ACF excesses in 10"<$θ$<90", the transition scale between 1- and 2-halo terms, suggestive of the existence of the non-linear halo bias effect. Combining the HOD models and previous clustering measurements of faint LBGs at z~4-7, we investigate dark-matter halo mass (Mh) of the z~4-7 LBGs and its correlation with various physical properties including the star-formation rate (SFR), the stellar-to-halo mass ratio (SHMR), and the dark matter accretion rate (dotMh) over a wide-mass range of Mh/M$_\odot$=4x10^10-4x10^12. We find that the SHMR increases from z~4 to 7 by a factor of ~4 at Mh~1x10^11 M$_\odot$, while the SHMR shows no strong evolution in the similar redshift range at Mh~1x10^12 M$_\odot$. Interestingly, we identify a tight relation of SFR/dotMh-Mh showing no significant evolution beyond 0.15 dex in this wide-mass range over z~4-7. This weak evolution suggests that the SFR/dotMh-Mh relation is a fundamental relation in high-redshift galaxy formation whose star formation activities are regulated by the dark matter mass assembly. Assuming this fundamental relation, we calculate the cosmic SFR densities (SFRDs) over z=0-10 (a.k.a. Madau-Lilly plot). The cosmic SFRD evolution based on the fundamental relation agrees with the one obtained by observations, suggesting that the cosmic SFRD increase from z~10 to 4-2 (decrease from z~4-2 to 0) is mainly driven by the increase of the halo abundance (the decrease of the accretion rate).

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The Nature of Massive Transition Galaxies in CANDELS, GAMA, and Cosmological Simulations

We explore observational and theoretical constraints on how galaxies might transition between the "star-forming main sequence" (SFMS) and varying "degrees of quiescence" out to $z=3$. Our analysis is focused on galaxies with stellar mass $M_*>10^{10}M_{\odot}$, and is enabled by GAMA and CANDELS observations, a semi-analytic model (SAM) of galaxy formation, and a cosmological hydrodynamical "zoom in" simulation with momentum-driven AGN feedback. In both the observations and the SAM, transition galaxies tend to have intermediate Sérsic indices, half-light radii, and surface stellar mass densities compared to star-forming and quiescent galaxies out to $z=3$. We place an observational upper limit on the average population transition timescale as a function of redshift, finding that the average high-redshift galaxy is on a "fast track" for quenching whereas the average low-redshift galaxy is on a "slow track" for quenching. We qualitatively identify four physical origin scenarios for transition galaxies in the SAM: oscillations on the SFMS, slow quenching, fast quenching, and rejuvenation. Quenching timescales in both the SAM and the hydrodynamical simulation are not fast enough to reproduce the quiescent population that we observe at $z\sim3$. In the SAM, we do not find a clear-cut morphological dependence of quenching timescales, but we do predict that the mean stellar ages, cold gas fractions, SMBH masses, and halo masses of transition galaxies tend to be intermediate relative to those of star-forming and quiescent galaxies at $z<3$.

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The Relationship between Galaxy and Dark Matter Halo Size from z~3 to the present

We explore empirical constraints on the statistical relationship between the radial size of galaxies and the radius of their host dark matter halos from $z\sim 0.1$--3 using the GAMA and CANDELS surveys. We map dark matter halo mass to galaxy stellar mass using relationships from abundance matching, applied to the Bolshoi-Planck dissipationless N-body simulation. We define SRHR$\equiv r_e/R_h$ as the ratio of galaxy radius to halo virial radius, and SRHR$λ\equiv r_e/(λR_h)$ as the ratio of galaxy radius to halo spin parameter times halo radius. At $z\sim 0.1$, we find an average value of SRHR $\simeq 0.018$ and SRHR$λ\simeq 0.5$ with very little dependence on stellar mass. SRHR and SRHR$λ$ have a weak dependence on cosmic time since $z\sim 3$. SRHR shows a mild decrease over cosmic time for low mass galaxies, but increases slightly or does not evolve for more massive galaxies. We find hints that at high redshift ($z\sim 2$--3), SRHR$λ$ is lower for more massive galaxies, while it shows no significant dependence on stellar mass at $z\lesssim 0.5$. We find that for both the GAMA and CANDELS samples, at all redshifts from $z\sim 0.1$--3, the observed conditional size distribution in stellar mass bins is remarkably similar to the conditional distribution of $λR_h$. We discuss the physical interpretation and implications of these results.

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Halo and Subhalo Demographics with Planck Cosmological Parameters: Bolshoi-Planck and MultiDark-Planck Simulations

We report and provide fitting functions for the abundance of dark matter halos and subhalos as a function of mass, circular velocity, and redshift from the new Bolshoi-Planck and MultiDark-Planck $Λ$CDM cosmological simulations, based on the Planck cosmological parameters. We also report the halo mass accretion rates, which may be connected with galaxy star formation rates. We show that the higher cosmological matter density of the Planck parameters compared with the WMAP parameters leads to higher abundance of massive halos at high redshifts. We find that the median halo spin parameter $λ_{\rm B} = J(2M_{\rm vir}R_{\rm vir}V_{\rm vir})^{-1}$ is nearly independent of redshift, leading to predicted evolution of galaxy sizes that is consistent with observations, while the significant decrease with redshift in median $λ_{\rm P} = J|E|^{-1/2}G^{-1}M^{-5/2}$ predicts more decrease in galaxy sizes than is observed. Using the Tully-Fisher and Faber-Jackson relations between galaxy velocity and mass, we show that a simple model of how galaxy velocity is related to halo maximum circular velocity leads to increasing overprediction of cosmic stellar mass density as redshift increases beyond redshifts $z\sim1$, implying that such velocity-mass relations must change at redshifts $z>1$. By making a realistic model of how observed galaxy velocities are related to halo circular velocity, we show that recent optical and radio observations of the abundance of galaxies are in good agreement with our $Λ$CDM simulations. Our halo demographics are based on updated versions of the \rockstar\ and \ctrees\ codes, and this paper includes appendices explaining all of their outputs. This paper is an introduction to a series of related papers presenting other analyses of the Bolshoi-Planck and MultiDark-Planck simulations.

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Clustering of quasars in the First Year of the SDSS-IV eBOSS survey: Interpretation and halo occupation distribution

In current and future surveys, quasars play a key role. The new data will extend our knowledge of the Universe as it will be used to better constrain the cosmological model at redshift $z>1$ via baryon acoustic oscillation and redshift space distortion measurements. Here, we present the first clustering study of quasars observed by the extended Baryon Oscillation Spectroscopic Survey. We measure the clustering of $\sim 70,000$ quasars located in the redshift range $0.9<z<2.2$ that cover 1,168 deg$^2$. We model the clustering and produce high-fidelity quasar mock catalogues based on the BigMultiDark Planck simulation. Thus, we use a modified (Sub)Halo Abundance Matching model to account for the specificities of the halo population hosting quasars. We find that quasars are hosted by halos with masses $\sim10^{12.7}M_\odot$ and their bias evolves from 1.54 ($z=1.06$) to 3.15 ($z=1.98$). Using the current eBOSS data, we cannot distinguish between models with different fractions of satellites. The high-fidelity mock light-cones, including properties of halos hosting quasars, are made publicly available.

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Properties of Dark Matter Halos as a Function of Local Environment Density

We study how properties of discrete dark matter halos depend on halo environment, characterized by the mass density around the halos on scales from 0.5 to 16 $h^{-1}{\rm Mpc}$. We find that low mass halos (those less massive than the characteristic mass $M_{\rm C}$ of halos collapsing at a given epoch) in high-density environments have lower accretion rates, lower spins, higher concentrations, and rounder shapes than halos in median density environments. Halos in median and low-density environments have similar accretion rates and concentrations, but halos in low density environments have lower spins and are more elongated. Halos of a given mass in high-density regions accrete material earlier than halos of the same mass in lower-density regions. All but the most massive halos in high-density regions are losing mass (i.e., being stripped) at low redshifts, which causes artificially lowered NFW scale radii and increased concentrations. Tidal effects are also responsible for the decreasing spins of low mass halos in high density regions at low redshifts $z < 1$, by preferentially removing higher angular momentum material from halos. Halos in low-density regions have lower than average spins because they lack nearby halos whose tidal fields can spin them up. We also show that the simulation density distribution is well fit by an Extreme Value Distribution, and that the density distribution becomes broader with cosmic time.

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Lensing is Low: Cosmology, Galaxy Formation, or New Physics?

We present high signal-to-noise galaxy-galaxy lensing measurements of the BOSS CMASS sample using 250 square degrees of weak lensing data from CFHTLenS and CS82. We compare this signal with predictions from mock catalogs trained to match observables including the stellar mass function and the projected and two dimensional clustering of CMASS. We show that the clustering of CMASS, together with standard models of the galaxy-halo connection, robustly predicts a lensing signal that is 20-40% larger than observed. Detailed tests show that our results are robust to a variety of systematic effects. Lowering the value of $S_{\rm 8}=σ_{\rm 8} \sqrt{Ω_{\rm m}/0.3}$ compared to Planck2015 reconciles the lensing with clustering. However, given the scale of our measurement ($r<10$ $h^{-1}$ Mpc), other effects may also be at play and need to be taken into consideration. We explore the impact of baryon physics, assembly bias, massive neutrinos, and modifications to general relativity on $ΔΣ$ and show that several of these effects may be non-negligible given the precision of our measurement. Disentangling cosmological effects from the details of the galaxy-halo connection, the effects of baryons, and massive neutrinos, is the next challenge facing joint lensing and clustering analyses. This is especially true in the context of large galaxy samples from Baryon Acoustic Oscillation surveys with precise measurements but complex selection functions.

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The evolution of star formation histories of quiescent galaxies

Although there has been much progress in understanding how galaxies evolve, we still do not understand how and when they stop forming stars and become quiescent. We address this by applying our galaxy spectral energy distribution models, which incorporate physically motivated star formation histories (SFHs) from cosmological simulations, to a sample of quiescent galaxies at $0.2<z<2.1$. A total of 845 quiescent galaxies with multi-band photometry spanning rest-frame ultraviolet through near-infrared wavelengths are selected from the CANDELS dataset. We compute median SFHs of these galaxies in bins of stellar mass and redshift. At all redshifts and stellar masses, the median SFHs rise, reach a peak, and then decline to reach quiescence. At high redshift, we find that the rise and decline are fast, as expected because the Universe is young. At low redshift, the duration of these phases depends strongly on stellar mass. Low-mass galaxies ($\log(M_{\ast}/M_{\odot})\sim9.5$) grow on average slowly, take a long time to reach their peak of star formation ($\gtrsim 4$ Gyr), and the declining phase is fast ($\lesssim 2$ Gyr). Conversely, high-mass galaxies ($\log(M_{\ast}/M_{\odot})\sim11$) grow on average fast ($\lesssim 2$ Gyr), and, after reaching their peak, decrease the star formation slowly ($\gtrsim 3$ Gyr). These findings are consistent with galaxy stellar mass being a driving factor in determining how evolved galaxies are, with high-mass galaxies being the most evolved at any time (i.e., downsizing). The different durations we observe in the declining phases also suggest that low- and high-mass galaxies experience different quenching mechanisms that operate on different timescales.

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The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Modeling the clustering and halo occupation distribution of BOSS-CMASS galaxies in the Final Data Release

We present a study of the clustering and halo occupation distribution of BOSS CMASS galaxies in the redshift range 0.43 < z < 0.7 drawn from the Final SDSS-III Data Release. We compare the BOSS results with the predictions of a Halo Abundance Matching (HAM) clustering model that assigns galaxies to dark matter halos selected from the large BigMultiDark $N$-body simulation of a flat $Λ$CDM Planck cosmology. We compare the observational data with the simulated ones on a light-cone constructed from 20 subsequent outputs of the simulation. Observational effects such as incompleteness, geometry, veto masks and fiber collisions are included in the model, which reproduces within 1-$σ$ errors the observed monopole of the 2-point correlation function at all relevant scales: from the smallest scales, 0.5 $h^{-1}$ Mpc, up to scales beyond the Baryonic Acoustic Oscillation feature. This model also agrees remarkably well with the BOSS galaxy power spectrum (up to $k\sim1$ $h$ Mpc$^{-1}$), and the Three-point correlation function. The quadrupole of the correlation function presents some tensions with observations. We discuss possible causes that can explain this disagreement, including target selection effects. Overall, the standard HAM model describes remarkably well the clustering statistics of the CMASS sample. We compare the stellar to halo mass relation for the CMASS sample measured using weak lensing in the CFHT Stripe 82 Survey with the prediction of our clustering model, and find a good agreement within 1-$σ$. The BigMD-BOSS light-cone including properties of BOSS galaxies and halo properties is made publicly available.

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Sussing Merger Trees: Stability and Convergence

Merger trees are routinely used to follow the growth and merging history of dark matter haloes and subhaloes in simulations of cosmic structure formation. Srisawat et al. (2013) compared a wide range of merger-tree-building codes. Here we test the influence of output strategies and mass resolution on tree-building. We find that, somewhat surprisingly, building the tree from more snapshots does not generally produce more complete trees; instead, it tends to short- en them. Significant improvements are seen for patching schemes which attempt to bridge over occasional dropouts in the underlying halo catalogues or schemes which combine the halo-finding and tree-building steps seamlessly. The adopted output strategy does not affec- t the average number of branches (bushiness) of the resultant merger trees. However, mass resolution has an influence on both main branch length and the bushiness. As the resolution increases, a halo with the same mass can be traced back further in time and will encounter more small progenitors during its evolutionary history. Given these results, we recommend that, for simulations intended as precursors for galaxy formation models where of order 100 or more snapshots are analysed, the tree-building routine should be integrated with the halo finder, or at the very least be able to patch over multiple adjacent snapshots.

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An Increasing Stellar Baryon Fraction in Bright Galaxies at High Redshift

Recent observations have shown that the characteristic luminosity of the rest-frame ultraviolet (UV) luminosity function does not significantly evolve at 4 < z < 7 and is approximately M*_UV ~ -21. We investigate this apparent non-evolution by examining a sample of 178 bright, M_UV < -21 galaxies at z=4 to 7, analyzing their stellar populations and host halo masses. Including deep Spitzer/IRAC imaging to constrain the rest-frame optical light, we find that M*_UV galaxies at z=4-7 have similar stellar masses of log(M/Msol)=9.6-9.9 and are thus relatively massive for these high redshifts. However, bright galaxies at z=4-7 are less massive and have younger inferred ages than similarly bright galaxies at z=2-3, even though the two populations have similar star formation rates and levels of dust attenuation. We match the abundances of these bright z=4-7 galaxies to halo mass functions from the Bolshoi Lambda-CDM simulation to estimate the halo masses. We find that the typical halo masses in ~M*_UV galaxies decrease from log(M_h/Msol)=11.9 at z=4 to log(M_h/Msol)=11.4 at z=7. Thus, although we are studying galaxies at a similar mass across multiple redshifts, these galaxies live in lower mass halos at higher redshift. The stellar baryon fraction in units of the cosmic mean Omega_b/Omega_m rises from 5.1% at z=4 to 11.7% at z=7; this evolution is significant at the ~3-sigma level. This rise does not agree with simple expectations of how galaxies grow, and implies that some effect, perhaps a diminishing efficiency of feedback, is allowing a higher fraction of available baryons to be converted into stars at high redshifts.

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Is Main Sequence Galaxy Star Formation Controlled by Halo Mass Accretion?

The galaxy stellar-to-halo mass relation (SHMR) is nearly time-independent for $z < 4$. We therefore construct a time-independent SHMR model for central galaxies, wherein the in-situ star formation rate (SFR) is determined by the halo mass accretion rate (MAR), which we call Stellar-Halo Accretion Rate Coevolution (SHARC). We show that the $\sim0.3$ dex dispersion of the halo MAR matches the observed dispersion of the SFR on the star-formation main sequence (MS). In the context of "bathtub"-type models of galaxy formation, SHARC leads to mass-dependent constraints on the relation between SFR and MAR. Despite its simplicity and the simplified treatment of mass growth from mergers, the SHARC model is likely to be a good approximation for central galaxies with $M_*=10^9- 10^{10.5}M_\odot$ that are on the MS, representing most of the star formation in the Universe. SHARC predictions agree with observed SFRs for galaxies on the MS at low redshifts, agree fairly well at $z\sim4$, but exceed observations at $z>4$. Assuming that the interstellar gas mass is constant for each galaxy (the "equilibrium condition" in bathtub models), the SHARC model allows calculation of net mass loading factors for inflowing and outflowing gas. With assumptions about preventive feedback based on simulations, SHARC allows calculation of galaxy metallicity evolution. If galaxy SFRs indeed track halo MARs, especially at low redshifts, that may help explain the success of models linking galaxy properties to halos (including age-matching) and the similarities between two-halo galaxy conformity and halo mass accretion conformity.

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On the Segregation of Dark Matter Substructure

We present the first comprehensive analysis of the segregation of dark matter subhaloes in their host haloes. Using numerical simulations, we examine the segregation of twelve different subhalo properties with respect to both orbital energy and halo-centric radius (in real space as well as in projection). Subhaloes are strongly segregated by accretion redshift, which is an outcome of the inside-out assembly of their host haloes. Since subhaloes that were accreted earlier have experienced more tidal stripping, subhaloes that have lost a larger fraction of their mass at infall are on more bound orbits. Subhaloes are also strongly segregated in their masses and maximum circular velocities at accretion. We demonstrate that part of this segregation is already imprinted in the infall conditions. For massive subhaloes it is subsequently boosted by dynamical friction, but only during their first radial orbit. The impact of these two effects is counterbalanced, though, by the fact that subhaloes with larger accretion masses are accreted later. Because of tidal stripping, subhaloes reveal little to no segregation by present-day mass or maximum circular velocity, while the corresponding torques cause subhaloes on more bound orbits to have smaller spin. There is a weak tendency for subhaloes that formed earlier to be segregated towards the center of their host halo, which is an indirect consequence of the fact that (sub)halo formation time is correlated with other, strongly segregated properties. We discuss the implications of our results for the segregation of satellite galaxies in galaxy groups and clusters.

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On The History and Future of Cosmic Planet Formation

We combine constraints on galaxy formation histories with planet formation models, yielding the Earth-like and giant planet formation histories of the Milky Way and the Universe as a whole. In the Hubble Volume (10^13 Mpc^3), we expect there to be ~10^20 Earth-like and ~10^20 giant planets; our own galaxy is expected to host ~10^9 and ~10^10 Earth-like and giant planets, respectively. Proposed metallicity thresholds for planet formation do not significantly affect these numbers. However, the metallicity dependence for giant planets results in later typical formation times and larger host galaxies than for Earth-like planets. The Solar System formed at the median age for existing giant planets in the Milky Way, and consistent with past estimates, formed after 80% of Earth-like planets. However, if existing gas within virialised dark matter haloes continues to collapse and form stars and planets, the Universe will form over 10 times more planets than currently exist. We show that this would imply at least a 92% chance that we are not the only civilisation the Universe will ever have, independent of arguments involving the Drake Equation.

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The Evolution of the Galaxy Rest-Frame Ultraviolet Luminosity Function Over the First Two Billion Years

We present a robust measurement and analysis of the rest-frame ultraviolet (UV) luminosity function at z=4-8. We use deep Hubble Space Telescope imaging over the CANDELS/GOODS fields, the Hubble Ultra Deep Field and the Year 1 Hubble Frontier Field deep parallel observations. These surveys provides an effective volume of 0.6-1.2 x 10^6 Mpc^3 over this epoch, allowing us to perform a robust search for faint (M_UV=-18) and bright (M_UV < -21) galaxies. We select candidate galaxies using a well-tested photometric redshift technique with careful screening of contaminants, finding a sample of 7446 galaxies at 3.5 1000 galaxies at z~6-8. We measure the luminosity function using a Markov Chain Monte Carlo analysis to measure robust uncertainties. At the faint end our results agree with previous studies, yet we find a higher abundance of UV-bright galaxies at z>6, with M* ~ -21 at z>5, different than that inferred based on previous trends at lower redshift. At z=8, a single power-law 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 to semi-analytical models, and find that the lack of evolution in M* is consistent with models where the impact of dust attenuation on the bright-end of the luminosity function decreases at higher redshift. We measure the evolution of the cosmic star-formation rate density, correcting for dust attenuation, and find that it declines as (1+z)^(-4.3 +/- 0.5) at z>4, consistent with observations at z>9. Our observations 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, 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. [abridged]

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