Halo Occupation Models Research Articles

The MillenniumTNG Project: an improved two-halo model for the galaxy–halo connection of red and blue galaxies

ABSTRACT Approximate methods to populate dark-matter haloes with galaxies are of great utility to galaxy surveys. However, the limitations of simple halo occupation models (HODs) preclude a full use of small-scale galaxy clustering data and call for more sophisticated models. We study two galaxy populations, luminous red galaxies (LRGs) and star-forming emission-line galaxies (ELGs), at two epochs, z = 1 and z = 0, in the large-volume, high-resolution hydrodynamical simulation of the MillenniumTNG project. In a partner study we concentrated on the small-scale, one-halo regime down to r ∼ 0.1 h−1 Mpc, while here we focus on modelling galaxy assembly bias in the two-halo regime, r ≳ 1 h−1 Mpc. Interestingly, the ELG signal exhibits scale dependence out to relatively large scales (r ∼ 20 h−1 Mpc), implying that the linear bias approximation for this tracer is invalid on these scales, contrary to common assumptions. The 10–15 per cent discrepancy is only reconciled when we augment our halo occupation model with a dependence on extrinsic halo properties (‘shear’ being the best-performing one) rather than intrinsic ones (e.g. concentration, peak mass). We argue that this fact constitutes evidence for two-halo galaxy conformity. Including tertiary assembly bias (i.e. a property beyond mass and ‘shear’) is not an essential requirement for reconciling the galaxy assembly bias signal of LRGs, but the combination of external and internal properties is beneficial for recovering ELG the clustering. We find that centrals in low-mass haloes dominate the assembly bias signal of both populations. Finally, we explore the predictions of our model for higher order statistics such as nearest neighbour counts. The latter supplies additional information about galaxy assembly bias and can be used to break degeneracies between halo model parameters.

The MillenniumTNG Project: refining the one-halo model of red and blue galaxies at different redshifts

ABSTRACT Luminous red galaxies (LRGs) and blue star-forming emission-line galaxies (ELGs) are key tracers of large-scale structure used by cosmological surveys. Theoretical predictions for such data are often done via simplistic models for the galaxy–halo connection. In this work, we use the large, high-fidelity hydrodynamical simulation of the MillenniumTNG project (MTNG) to inform a new phenomenological approach for obtaining an accurate and flexible galaxy-halo model on small scales. Our aim is to study LRGs and ELGs at two distinct epochs, z = 1 and z = 0, and recover their clustering down to very small scales, $r \sim 0.1 \ h^{-1}\, {\rm Mpc}$, i.e. the one-halo regime, while a companion paper extends this to a two-halo model for larger distances. The occupation statistics of ELGs in MTNG inform us that (1) the satellite occupations exhibit a slightly super-Poisson distribution, contrary to commonly made assumptions, and (2) that haloes containing at least one ELG satellite are twice as likely to host a central ELG. We propose simple recipes for modelling these effects, each of which calls for the addition of a single free parameter to simpler halo occupation models. To construct a reliable satellite population model, we explore the LRG and ELG satellite radial and velocity distributions and compare them with those of subhaloes and particles in the simulation. We find that ELGs are anisotropically distributed within haloes, which together with our occupation results provides strong evidence for cooperative galaxy formation (manifesting itself as one-halo galaxy conformity); i.e. galaxies with similar properties form in close proximity to each other. Our refined galaxy-halo model represents a useful improvement of commonly used analysis tools and thus can be of help to increase the constraining power of large-scale structure surveys.

SimBIG: mock challenge for a forward modeling approach to galaxy clustering

Simulation-Based Inference of Galaxies (SimBIG) is a forward modeling framework for analyzing galaxy clustering using simulation-based inference. In this work, we present the SimBIG forward model, which is designed to match the observed SDSS-III BOSS CMASS galaxy sample. The forward model is based on high-resolution Quijote N-body simulations and a flexible halo occupation model. It includes full survey realism and models observational systematics such as angular masking and fiber collisions. We present the “mock challenge” for validating the accuracy of posteriors inferred from SimBIG using a suite of 1,500 test simulations constructed using forward models with a different N-body simulation, halo finder, and halo occupation prescription. As a demonstration of SimBIG, we analyze the power spectrum multipoles out to k max = 0.5 h/Mpc and infer the posterior of ΛCDM cosmological and halo occupation parameters. Based on the mock challenge, we find that our constraints on Ω m and σ 8 are unbiased, but conservative. Hence, the mock challenge demonstrates that SimBIG provides a robust framework for inferring cosmological parameters from galaxy clustering on non-linear scales and a complete framework for handling observational systematics. In subsequent work, we will use SimBIG to analyze summary statistics beyond the power spectrum including the bispectrum, marked power spectrum, skew spectrum, wavelet statistics, and field-level statistics.

A machine learning approach to mapping baryons on to dark matter haloes using the eagle and C-EAGLE simulations

ABSTRACT High-resolution cosmological hydrodynamic simulations are currently limited to relatively small volumes due to their computational expense. However, much larger volumes are required to probe rare, overdense environments, and measure clustering statistics of the large-scale structure. Typically, zoom simulations of individual regions are used to study rare environments, and semi-analytic models and halo occupation models applied to dark-matter-only (DMO) simulations are used to study the Universe in the large-volume regime. We propose a new approach, using a machine learning framework, to explore the halo–galaxy relationship in the periodic eagle simulations, and zoom C-EAGLE simulations of galaxy clusters. We train a tree-based machine learning method to predict the baryonic properties of galaxies based on their host dark matter halo properties. The trained model successfully reproduces a number of key distribution functions for an infinitesimal fraction of the computational cost of a full hydrodynamic simulation. By training on both periodic simulations and zooms of overdense environments, we learn the bias of galaxy evolution in differing environments. This allows us to apply the trained model to a larger DMO volume than would be possible if we only trained on a periodic simulation. We demonstrate this application using the (800 Mpc)3 P-Millennium simulation, and present predictions for key baryonic distribution functions and clustering statistics from the eagle model in this large volume.

PRIMUS: Clustering of Star-forming and Quiescent Central Galaxies at 0.2 < z < 0.9

Abstract Previous work has demonstrated that at a given stellar mass, quiescent galaxies are more strongly clustered than star-forming galaxies. The contribution to this signal from central, as opposed to satellite, galaxies is not known, which has strong implications for galaxy evolution models. To investigate the contribution from central galaxies, here we present measurements of the clustering of isolated primary (IP) galaxies, used as a proxy for central galaxies, at 0.2 < z < 0.9 with data from the PRIsm MUlti-Object Survey (PRIMUS) galaxy redshift survey. Using a sample of spectroscopic redshifts for ∼60,000 galaxies with covering 5 deg2 on the sky, we define IP galaxies using isolation cuts in spatial proximity and stellar mass of nearby galaxies. We find that at a fixed stellar mass, quiescent IP galaxies are more strongly clustered than star-forming IP galaxies at z ∼ 0.35 (10σ). Using mock galaxy catalogs based on the recent halo occupation models of Behroozi et al. and designed to replicate the parameters of the PRIMUS survey data set, we find that these clustering differences are due in part to quiescent central galaxies being more strongly clustered than star-forming central galaxies. This is consistent with either distinct stellar-to-halo mass relations for quiescent and star-forming central galaxies, and/or central galaxy assembly bias. We additionally use mock catalogs to assess the dependence of both incompleteness and satellite galaxy contamination in the IP galaxy samples on redshift, galaxy type, and stellar mass, and demonstrate how isolation criteria yield biased subsamples of central galaxies via environmental incompleteness, or the preferential exclusion of central galaxies in overdense environments.

How to optimally constrain galaxy assembly bias: supplement projected correlation functions with count-in-cells statistics

ABSTRACT Most models for the statistical connection between galaxies and their haloes ignore the possibility that galaxy properties may be correlated with halo properties other than halo mass, a phenomenon known as galaxy assembly bias. And yet, it is known that such correlations can lead to systematic errors in the interpretation of survey data that are analysed using traditional halo occupation models. At present, the degree to which galaxy assembly bias may be present in the real Universe, and the best strategies for constraining it remain uncertain. We study the ability of several observables to constrain galaxy assembly bias from redshift survey data using the decorated halo occupation distribution (dHOD), an empirical model of the galaxy–halo connection that incorporates assembly bias. We cover an expansive set of observables, including the projected two-point correlation function $w$p(rp), the galaxy–galaxy lensing signal ΔΣ(rp), the void probability function VPF(r), the distributions of counts-in-cylinders P(NCIC), and counts-in-annuli P(NCIA), and the distribution of the ratio of counts in cylinders of different sizes P(N2/N5). We find that despite the frequent use of the combination $w$p(rp) + ΔΣ(rp) in interpreting galaxy data, the count statistics, P(NCIC) and P(NCIA), are generally more efficient in constraining galaxy assembly bias when combined with $w$p(rp). Constraints based upon $w$p(rp) and ΔΣ(rp) share common degeneracy directions in the parameter space, while combinations of $w$p(rp) with the count statistics are more complementary. Therefore, we strongly suggest that count statistics should be used to complement the canonical observables in future studies of the galaxy–halo connection.

How Are Galaxies Assigned to Halos? Searching for Assembly Bias in the SDSS Galaxy Clustering

Abstract Clustering of dark matter halos has been shown to depend on halo properties beyond mass, such as halo concentration, a phenomenon referred to as halo assembly bias. Standard halo-occupation models (HOD) in large-scale structure studies assume that halo mass alone is sufficient in characterizing the connection between galaxies and halos. Modeling of galaxy clustering can face systematic effects if the number of galaxies within a halo is correlated with other halo properties. Using the Small MultiDark-Planck high-resolution N-body simulation and the clustering measurements of the Sloan Digital Sky Survey DR7 main galaxy sample, we investigate the extent to which the concentration dependence of halo occupation can be constrained. Furthermore, we study how allowing for the concentration dependence can improve our modeling of galaxy clustering. Our constraints on HOD with assembly bias suggest that satellite population is not correlated with halo concentration at fixed halo mass. At fixed halo mass, our constraints favor lack of correlation between the occupation of centrals and halo concentration in the most luminous samples (M r < −21.5, −21), and modest correlation in the M r < −20.5, −20, −19.5 samples. We show that, in comparison with abundance-matching mock catalogs, our findings suggest qualitatively similar but modest levels of the impact of halo assembly bias on galaxy clustering. The effect is only present in the central occupation and becomes less significant in brighter galaxy samples. Furthermore, by performing model comparison based on information criteria, we find that in most cases, the standard mass-only HOD model is still favored by the observations.

Intensity mapping cross-correlations II: HI halo models including shot noise

HI intensity mapping data traces the large-scale structure matter distribution using the integrated emission of neutral hydrogen gas (HI). The cross-correlation of the intensity maps with optical galaxy surveys can mitigate foreground and systematic effects, but has been shown to significantly depend on galaxy evolution parameters of the HI and the optical sample. Previously, we have shown that the shot noise of the cross-correlation scales with the HI content of the optical samples, such that the shot noise estimation infers the average HI masses of these samples. In this article, we present an adaptive framework for the cross-correlation of HI intensity maps with galaxy samples using our implementation of the halo model formalism (Murray et al 2018, in prep) which utilises the halo occupation distribution of galaxies to predict their power spectra. We compare two HI population models, tracing the spatial halo and the galaxy distribution respectively, and present their auto- and cross-power spectra with an associated galaxy sample. We find that the choice of the HI model and the distribution of the HI within the galaxy sample have minor significance for the shape of the auto- and cross-correlations, but highly impact the measured shot noise amplitude of the estimators, a finding we confirm with simulations. We demonstrate parameter estimation of the HI halo occupation models and advocate this framework for the interpretation of future experimental data, with the prospect of determining the HI masses of optical galaxy samples via the cross-correlation shot noise.

Unveiling galaxy bias via the halo model, KiDS, and GAMA

We measure the projected galaxy clustering and galaxy-galaxy lensing signals using the Galaxy And Mass Assembly (GAMA) survey and Kilo-Degree Survey (KiDS) to study galaxy bias. We use the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics to constrain the parameters of the halo occupation statistics and to unveil the origin of galaxy biasing. The bias function $\Gamma_{\text{gm}}(r_{\text{p}})$, where $r_{\text{p}}$ is the projected comoving separation, is evaluated using the analytical halo model from which the scale dependence of $\Gamma_{\text{gm}}(r_{\text{p}})$, and the origin of the non-linearity and stochasticity in halo occupation models can be inferred. Our observations unveil the physical reason for the non-linearity and stochasticity, further explored using hydrodynamical simulations, with the stochasticity mostly originating from the non-Poissonian behaviour of satellite galaxies in the dark matter haloes and their spatial distribution, which does not follow the spatial distribution of dark matter in the halo. The observed non-linearity is mostly due to the presence of the central galaxies, as was noted from previous theoretical work on the same topic. We also see that overall, more massive galaxies reveal a stronger scale dependence, and out to a larger radius. Our results show that a wealth of information about galaxy bias is hidden in halo occupation models. These models should therefore be used to determine the influence of galaxy bias in cosmological studies.

Disruption of dark matter substructure: fact or fiction?

Accurately predicting the demographics of dark matter (DM) substructure is of paramount importance for many fields of astrophysics, including gravitational lensing, galaxy evolution, halo occupation modeling, and constraining the nature of dark matter. Because of its strongly non-linear nature, DM substructure is typically modeled using N-body simulations, which reveal that large fractions of DM subhaloes undergo complete disruption. In this paper we use both analytical estimates and idealized numerical simulations to investigate whether this disruption is mainly physical, due to tidal heating and stripping, or numerical (i.e., artificial). We show that, contrary to naive expectation, subhaloes that experience a tidal shock $\Delta E$ that exceeds the subhalo's binding energy, $|E_{\rm b}|$, do not undergo disruption, even when $\Delta E/|E_{\rm b}|$ is as large as 100. Along the same line, and contrary to existing claims in the literature, instantaneously stripping matter from the outskirts of a DM subhalo also does not result in its complete disruption, even when the instantaneous remnant has positive binding energy. In addition, we show that tidal heating due to high-speed (impulsive) encounters with other subhaloes (`harassment'), is negligible compared to the tidal effects due to the host halo. Hence, we conclude that, in the absence of baryonic processes, the complete, physical disruption of CDM substructure is extremely rare, and that most disruption in numerical simulations therefore must be artificial. We discuss various processes that have been associated with numerical overmerging, and conclude that inadequate force-softening is the most likely culprit.

LUMINOUS AND DARK MATTER PROFILES FROM GALAXIES TO CLUSTERS: BRIDGING THE GAP WITH GROUP-SCALE LENSES

Observations of strong gravitational lensing, stellar kinematics, and larger-scale tracers enable accurate measures of the distribution of dark matter (DM) and baryons in massive early-type galaxies (ETGs). While such techniques have been applied to galaxy-scale and cluster-scale lenses, the paucity of intermediate-mass systems with high-quality data has precluded a uniform analysis of mass-dependent trends. With the aim of bridging this gap, we present new observations and analyses of 10 group-scale lenses at 〈z 〉= 0.36 characterized by Einstein radii θ_(Ein) = 2.5 − 5.1 and a mean halo mass of M_(200) = 10^(14.0)M_⊙. For these groups, we find a mean halo concentration c_(200) = 5.0 ± 0.8 consistent with unmodified cold dark matter halos. By combining our data with other lens samples, we analyze the mass structure of ETGs in halos spanning the mass range 10^(13) M_⊙ − 10^(15)M_⊙ halos using homogeneous techniques. We show that the slope of the total density profile γtot within the effective radius depends on the stellar surface density, as demonstrated previously, but also on the halo mass. We analyze these trends using halo occupation models and resolved stellar kinematics with the goal of testing the universality of the DM profile. Whereas the central galaxies of clusters require a shallow inner DM density profile, group-scale lenses are consistent with a Navarro–Frenk–White profile or one that is slightly contracted. The largest uncertainties arise from the sample size and likely radial gradients in stellar populations. We conclude that the net effect of baryons on the DM distribution may not be universal, but more likely varies with halo mass due to underlying trends in star formation efficiency and assembly history.

DARK MATTER HALO MODELS OF STELLAR MASS-DEPENDENT GALAXY CLUSTERING IN PRIMUS+DEEP2 AT 0.2 <z< 1.2

We utilize $\Lambda$CDM halo occupation models of galaxy clustering to investigate the evolving stellar mass dependent clustering of galaxies in the PRIsm MUlti-object Survey (PRIMUS) and DEEP2 Redshift Survey over the past eight billion years of cosmic time, between $0.2<z<1.2$. These clustering measurements provide new constraints on the connections between dark matter halo properties and galaxy properties in the context of the evolving large-scale structure of the universe. Using both an analytic model and a set of mock galaxy catalogs, we find a strong correlation between central galaxy stellar mass and dark matter halo mass over the range $M_\mathrm{halo}\sim10^{11}$-$10^{13}~h^{-1}M_\odot$, approximately consistent with previous observations and theoretical predictions. However, the stellar-to-halo mass relation (SHMR) and the mass scale where star formation efficiency reaches a maximum appear to evolve more strongly than predicted by other models, including models based primarily on abundance-matching constraints. We find that the fraction of satellite galaxies in haloes of a given mass decreases significantly from $z\sim0.5$ to $z\sim0.9$, partly due to the fact that haloes at fixed mass are rarer at higher redshift and have lower abundances. We also find that the $M_1/M_\mathrm{min}$ ratio, a model parameter that quantifies the critical mass above which haloes host at least one satellite, decreases from $\approx20$ at $z\sim0$ to $\approx13$ at $z\sim0.9$. Considering the evolution of the subhalo mass function vis-\`{a}-vis satellite abundances, this trend has implications for relations between satellite galaxies and halo substructures and for intracluster mass, which we argue has grown due to stripped and disrupted satellites between $z\sim0.9$ and $z\sim0.5$.

Galaxy Cluster Mass Reconstruction Project – II. Quantifying scatter and bias using contrasting mock catalogues

This article is the second in a series in which we perform an extensive comparison of various galaxy-based cluster mass estimation techniques that utilise the positions, velocities and colours of galaxies. Our aim is to quantify the scatter, systematic bias and completeness of cluster masses derived from a diverse set of 25 galaxy-based methods using two contrasting mock galaxy catalogues based on a sophisticated halo occupation model and a semi-analytic model. Analysing 968 clusters, we find a wide range in the RMS errors in log M200c delivered by the different methods (0.18 to 1.08 dex, i.e., a factor of ~1.5 to 12), with abundance matching and richness methods providing the best results, irrespective of the input model assumptions. In addition, certain methods produce a significant number of catastrophic cases where the mass is under- or over-estimated by a factor greater than 10. Given the steeply falling high-mass end of the cluster mass function, we recommend that richness or abundance matching-based methods are used in conjunction with these methods as a sanity check for studies selecting high mass clusters. We see a stronger correlation of the recovered to input number of galaxies for both catalogues in comparison with the group/cluster mass, however, this does not guarantee that the correct member galaxies are being selected. We do not observe significantly higher scatter for either mock galaxy catalogues. Our results have implications for cosmological analyses that utilise the masses, richnesses, or abundances of clusters, which have different uncertainties when different methods are used.

Tidal-induced lopsidedness in Magellanic-type galaxies

We investigate the tidally induced conversion of barred late-type spirals to Magellanic-type discs with numerical simulations, to establish how the lifetime of lopsidedness (asymmetry) varies with numerical parametrizations. Using a reference model based on observed properties of the Large Magellanic Cloud (LMC), we show that its off-centre bar, one-arm spiral and one-sided star formation can be induced by a brief tidal interaction. We thereafter perform a detailed parameter study, and find that at the dynamical mass of LMC-type discs (∼1010 M⊙), stellar lopsidedness (as quantified by the m = 1 Fourier mode) and bar off-centredness can vary widely in amplitude, but are generally short-lived (∼Gyr). Tidal interactions induce more persistent lopsidedness in lower mass galaxies (several Gyr), in particular those with large halo-to-disc mass ratios as implied by recent halo occupation models. We suggest that the tidal interactions play a larger role in the observed ubiquity of lopsidedness than the presently favoured gas accretion mechanism for lower mass galaxies. Other characteristics of Magellanic-type galaxies, such as one-sided star formation, are quantified and tend to arise more prominently in discs with later-type spiral structure (more halo-dominated inner disc, weaker bars) following retrograde orbital encounters.

On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model

Galaxies are (biased) tracers of the dark matter in theUniverse. This mapping can be conveniently divided into two parts: the connection between galaxies and dark matter haloes (halo occupation statistics) and the relation between haloes and the underlying matter distribution. The former is the focus of this paper in which we formulate the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics. Using two-point statistics in projection, we define the galaxy bias function, bg(rp), and the galaxy–dark matter cross-correlation function, , where rp is the projected distance. We use the analytical halo model to predict how the scale dependence of is the projected distance. We use the analytical halo model to predict how the scale dependence of bg and , over the range 0.1 ≲ rp ≲ 30 h−1 Mpc, depends on the non-linearity and stochasticity in halo occupation models. In particular, we quantify the effect due to the presence of central galaxies, the assumption for the radial distribution of satellite galaxies, the richness of the halo and the Poisson character of the probability to have a certain number of satellite galaxies in the halo of a certain mass. Overall, brighter galaxies reveal a stronger scale dependence, and out to a larger radius. In real space, we find that galaxy bias becomes scale independent, with Mpc, depending on luminosity. However, galaxy bias is scale dependent out to much larger radii when one uses the projected quantities defined in this paper. These projected bias functions have the advantage that they are more easily accessible observationally and that their scale dependence carries a wealth of information regarding the properties of galaxy biasing. To observationally constrain the parameters of the halo model and to unveil the origin of galaxy biasing, we propose the use of the bias function . This function is obtained via a combination of weak gravitational lensing and galaxy clustering, and it can be measured using existing and forthcoming imaging and spectroscopic galaxy surveys.

Galaxy Zoo: the environmental dependence of bars and bulges in disc galaxies

We present an analysis of the environmental dependence of bars and bulges in disc galaxies, using a volume-limited catalogue of 15 810 galaxies at z < 0.06 from the Sloan Digital Sky Survey with visual morphologies from the Galaxy Zoo 2 project. We find that the likelihood of having a bar, or bulge, in disc galaxies increases when the galaxies have redder (optical) colours and larger stellar masses, and observe a transition in the bar and bulge likelihoods at M*= 2 × 1010 M⊙, such that massive disc galaxies are more likely to host bars and bulges. In addition, while some barred and most bulge-dominated galaxies are on the ‘red sequence’ of the colour–magnitude diagram, we see a wider variety of colours for galaxies that host bars. We use galaxy clustering methods to demonstrate statistically significant environmental correlations of barred, and bulge-dominated, galaxies, from projected separations of 150 kpc h−1 to 3 Mpc h−1. These environmental correlations appear to be independent of each other: i.e. bulge-dominated disc galaxies exhibit a significant bar–environment correlation, and barred disc galaxies show a bulge–environment correlation. As a result of sparse sampling tests – our sample is nearly 20 times larger than those used previously – we argue that previous studies that did not detect a bar–environment correlation were likely inhibited by small number statistics. We demonstrate that approximately half of the bar–environment correlation can be explained by the fact that more massive dark matter haloes host redder disc galaxies, which are then more likely to have bars; this fraction is estimated to be 50 ± 10 per cent from a mock catalogue analysis and 60 ± 5 per cent from the data. Likewise, we show that the environmental dependence of stellar mass can only explain a smaller fraction (25 ± 10 per cent) of the bar–environment correlation. Therefore, a significant fraction of our observed environmental dependence of barred galaxies is not due to colour or stellar mass dependences, and hence must be due to another galaxy property, such as gas content, or to environmental influences. Finally, by analysing the projected clustering of barred and unbarred disc galaxies with halo occupation models, we argue that barred galaxies are in slightly higher mass haloes than unbarred ones, and some of them (approximately 25 per cent) are satellite galaxies in groups. We discuss the implications of our results on the effects of minor mergers and interactions on bar formation in disc galaxies.

Angular correlation function of 1.5 million luminous red galaxies: clustering evolution and a search for baryon acoustic oscillations

We present the angular correlation function measured from photometric samples comprising 1562 800 luminous red galaxies (LRGs). Three LRG samples were extracted from the Sloan Digital Sky Survey (SDSS) imaging data, based on colour-cut selections at redshifts, z≈ 0.35, 0.55 and 0.7 as calibrated by the spectroscopic surveys, SDSS-LRG, 2dF-SDSS LRG and QSO (quasi-stellar object) (2SLAQ) and the AAΩ-LRG survey. The galaxy samples cover ≈7600 deg2 of sky, probing a total cosmic volume of ≈5.5 h−3 Gpc3. The small- and intermediate-scale correlation functions generally show significant deviations from a single power-law fit with a well-detected break at ≈1 h−1 Mpc, consistent with the transition scale between the one- and two-halo terms in halo occupation models. For galaxy separations 1–20 h−1 Mpc and at fixed luminosity, we see virtually no evolution of the clustering with redshift and the data are consistent with a simple high peaks biasing model where the comoving LRG space density is constant with z. At fixed z, the LRG clustering amplitude increases with luminosity in accordance with the simple high peaks model, with a typical LRG dark matter halo mass 1013–1014h−1 M⊙. For r < 1 h−1 Mpc, the evolution is slightly faster and the clustering decreases towards high redshift consistent with a virialized clustering model. However, assuming the halo occupation distribution (HOD) and Λ cold dark matter (ΛCDM) halo merger frameworks, ∼2–3 per cent/Gyr of the LRGs are required to merge in order to explain the small scales clustering evolution, consistent with previous results. At large scales, our result shows good agreement with the SDSS-LRG result of Eisenstein et al. but we find an apparent excess clustering signal beyond the baryon acoustic oscillations (BAO) scale. Angular power spectrum analyses of similar LRG samples also detect a similar apparent large-scale clustering excess but more data are required to check for this feature in independent galaxy data sets. Certainly, if the ΛCDM model were correct then we would have to conclude that this excess was caused by systematics at the level of Δw≈ 0.001–0.0015 in the photometric AAΩ-LRG sample.

Properties of dark matter haloes and their correlations: the lesson from principal component analysis

We study the correlations between the structural parameters of dark matter haloes using principal component analysis. We consider a set of eight parameters, six of which are commonly used to characterize dark matter halo properties: mass, concentration, spin, shape, overdensity and the angle (ΦL) between the major axis and the angular momentum vector. Two additional parameters (xoff and ρrms) are used to describe the degree of ‘relaxedness’ of the halo. We find that we can account for much of the variance of these properties with halo mass and concentration, on the one hand, and halo relaxedness on the other. None the less, three principal components are usually required to account for most of the variance. We argue that halo mass is not as dominant as expected, which is a challenge for halo occupation models and semi-analytic models that assume that mass determines other halo (and galaxy) properties. In addition, we find that the angle ΦL is not significantly correlated with other halo parameters, which may present a difficulty for models in which galaxy discs are oriented in haloes in a particular way. Finally, at fixed mass, we find that a halo’s environment (quantified by the large-scale overdensity) is relatively unimportant.

A COSMIC VARIANCE COOKBOOK

Deep pencil beam surveys (<1 deg^2) are of fundamental importance for studying the high-redshift universe. However, inferences about galaxy population properties are in practice limited by 'cosmic variance'. This is the uncertainty in observational estimates of the number density of galaxies arising from the underlying large-scale density fluctuations. This source of uncertainty can be significant, especially for surveys which cover only small areas and for massive high-redshift galaxies. Cosmic variance for a given galaxy population can be determined using predictions from cold dark matter theory and the galaxy bias. In this paper we provide tools for experiment design and interpretation. For a given survey geometry we present the cosmic variance of dark matter as a function of mean redshift z and redshift bin size Dz. Using a halo occupation model to predict galaxy clustering, we derive the galaxy bias as a function of mean redshift for galaxy samples of a given stellar mass range. In the linear regime, the cosmic variance of these galaxy samples is the product of the galaxy bias and the dark matter cosmic variance. We present a simple recipe using a fitting function to compute cosmic variance as a function of the angular dimensions of the field, z, Dz and stellar mass m*. We also provide tabulated values and a software tool. We find that for GOODS at z=2 and with Dz=0.5 the relative cosmic variance of galaxies with m*>10^11 Msun is ~38%, while it is ~27% for GEMS and ~12% for COSMOS. For galaxies of m*~10^10 Msun the relative cosmic variance is ~19% for GOODS, ~13% for GEMS and ~6% for COSMOS. This implies that cosmic variance is a significant source of uncertainty at z=2 for small fields and massive galaxies, while for larger fields and intermediate mass galaxies cosmic variance is less serious.

BINARY QUASARS AT HIGH REDSHIFT. II. SUB-Mpc CLUSTERING ATz∼ 3-4

We present measurements of the small-scale (0.1<~ r <~ 1 Mpc/h) quasar two-point correlation function at z>2.9, for a flux-limited (i<21) sample of 15 binary quasars compiled by Hennawi et al. (2009). The amplitude of the small-scale clustering increases from z ~ 3 to z ~ 4. The small-scale clustering amplitude is comparable to or lower than power-law extrapolations (with slope gamma=2) from the large-scale correlation function of the i<20.2 quasar sample from the Sloan Digital Sky Survey. Using simple prescriptions relating quasars to dark matter halos, we model the observed small-scale clustering with halo occupation models. Reproducing the large-scale clustering amplitude requires that the active fraction of the black holes in the central galaxies of halos is near unity, but the level of small-scale clustering favors an active fraction of black holes in satellite galaxies 0.1 <~ f_s <~ 0.5 at z >~ 3.