Mock Surveys Research Articles

Cosmological constraints from a combination of galaxy clustering and lensing – I. Theoretical framework

We present a new method that simultaneously solves for cosmology and galaxy bias on non-linear scales. The method uses the halo model to analytically describe the (non-linear) matter distribution, and the conditional luminosity function (CLF) to specify the halo occupation statistics. For a given choice of cosmological parameters, this model can be used to predict the galaxy luminosity function, as well as the two-point correlation functions of galaxies, and the galaxy–galaxy lensing signal, both as a function of scale and luminosity. These observables have been reliably measured from the Sloan Digital Sky Survey. In this paper, the first in a series, we present the detailed, analytical model, which we test against mock galaxy redshift surveys constructed from high-resolution numerical N-body simulations. We demonstrate that our model, which includes scale dependence of the halo bias and a proper treatment of halo exclusion, reproduces the three-dimensional galaxy–galaxy correlation and the galaxy–matter cross-correlation (which can be projected to predict the observables) with an accuracy better than 10 (in most cases 5) per cent. Ignoring either of these effects, as is often done, results in systematic errors that easily exceed 40 per cent on scales of ∼ 1 h− 1 Mpc, where the data are typically most accurate. Finally, since the projected correlation functions of galaxies are never obtained by integrating the redshift-space correlation function along the line of sight out to infinity, simply because the data only cover a finite volume, they are still affected by residual redshift-space distortions (RRSDs). Ignoring these, as done in numerous studies in the past, results in systematic errors that easily exceed 20 per cent on large scales (rp ≳ 10 h− 1 Mpc). We show that it is fairly straightforward to correct for these RRSDs, to an accuracy better than ∼ 2 per cent, using a mildly modified version of the linear Kaiser formalism.

Reconstructing cosmological initial conditions from galaxy peculiar velocities – I. Reverse Zeldovich Approximation

We propose a new method to recover the cosmological initial conditions of the presently observed galaxy distribution, which can serve to run constrained simulations of the Local Universe. Our method, the Reverse Zeldovich Approximation (RZA), can be applied to radial galaxy peculiar velocity data and extends the previously used Constrained Realizations (CR) method by adding a Lagrangian reconstruction step. The RZA method consists of applying the Zeldovich approximation in reverse to galaxy peculiar velocities to estimate the cosmic displacement field and the initial linear matter distribution from which the present-day Local Universe evolved.We test our method with a mock survey taken from a cosmological simulation. We show that the halo peculiar velocities at z = 0 are close to the linear prediction of the Zeldovich approximation, if a grouping is applied to the data to remove virial motions. We find that the addition of RZA to the CR method significantly improves the reconstruction of the initial conditions. The RZA is able to recover the correct initial positions of the velocity tracers with a median error of only 1.36 Mpc/h in our test simulation. For realistic sparse and noisy data, this median increases to 5 Mpc/h. This is a significant improvement over the previous approach of neglecting the displacement field, which introduces errors on a scale of 10 Mpc/h or even higher. Applying the RZA method to the upcoming high-quality observational peculiar velocity catalogues will generate much more precise constrained simulations of the Local Universe.

An electronic system to collect distance‐sampling data during helicopter surveys of northern bobwhite

AbstractDistance sampling during aerial surveys has been used extensively to estimate the density of many wildlife species. However, practical issues arise when using distance sampling during aerial surveys, such as obtaining accurate perpendicular distances. We assembled a computerized, electronic system to collect distance‐sampling data (e.g., transect length, detection location, and perpendicular distance) during aerial surveys. We tested the accuracy of the system in a controlled trial and a mock survey. We also evaluated the electronic system during field surveys of northern bobwhite (Colinus virginianus) conducted in the Rio Grande Plains and Rolling Plains ecoregions of Texas, USA, during December 2007–2008. For comparison, we evaluated the accuracy of visual estimation of distance during a mock survey. A strong linear relationship existed between estimated and actual distances for the controlled trial (r2 = 0.99) and mock survey (r2 = 0.98) using the electronic system. Perpendicular‐distance error (i.e., absolute difference between estimated distance and actual distance) for the electronic system was low during the controlled trial (1.4 ± 0.4 m; ${\bar {x}}$ ± SE) and mock survey (3.0 ± 0.5 m) but not during the visual estimation of distance (10 ± 1.5 m). Estimates of bobwhite density obtained using the electronic system exhibited reasonable precision for each ecoregion during both years (CV < 20%). Perpendicular‐distance error slightly increased with target distance (0.7‐m increase in error for every 10‐m increase in target distance). Overall, the electronic system appears to be a promising technique to estimate density of northern bobwhite and possibly other terrestrial species for which aerial‐based distance sampling is appropriate. © The Wildlife Society, 2012

PHOTOMETRIC SUPERNOVA COSMOLOGY WITH BEAMS AND SDSS-II

Supernova cosmology without spectroscopic confirmation is an exciting new frontier which we address here with the Bayesian Estimation Applied to Multiple Species (BEAMS) algorithm and the full three years of data from the Sloan Digital Sky Survey II Supernova Survey (SDSS-II SN). BEAMS is a Bayesian framework for using data from multiple species in statistical inference when one has the probability that each data point belongs to a given species, corresponding in this context to different types of supernovae with their probabilities derived from their multi-band lightcurves. We run the BEAMS algorithm on both Gaussian and more realistic SNANA simulations with of order 10^4 supernovae, testing the algorithm against various pitfalls one might expect in the new and somewhat uncharted territory of photometric supernova cosmology. We compare the performance of BEAMS to that of both mock spectroscopic surveys and photometric samples which have been cut using typical selection criteria. The latter typically are either biased due to contamination or have significantly larger contours in the cosmological parameters due to small data-sets. We then apply BEAMS to the 792 SDSS-II photometric supernovae with host spectroscopic redshifts. In this case, BEAMS reduces the area of the (\Omega_m,\Omega_\Lambda) contours by a factor of three relative to the case where only spectroscopically confirmed data are used (297 supernovae). In the case of flatness, the constraints obtained on the matter density applying BEAMS to the photometric SDSS-II data are \Omega_m(BEAMS)=0.194\pm0.07. This illustrates the potential power of BEAMS for future large photometric supernova surveys such as LSST.

Orca: The Overdense Red-sequence Cluster Algorithm

We present a new cluster detection algorithm designed for the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) survey but with generic application to any multiband data. The method makes no prior assumptions about the properties of clusters other than (a) the similarity in colour of cluster galaxies (the "red sequence") and (b) an enhanced projected surface density. The detector has three main steps: (i) it identifies cluster members by photometrically filtering the input catalogue to isolate galaxies in colour-magnitude space, (ii) a Voronoi diagram identifies regions of high surface density, (iii) galaxies are grouped into clusters with a Friends-of-Friends technique. Where multiple colours are available, we require systems to exhibit sequences in two colours. In this paper we present the algorithm and demonstrate it on two datasets. The first is a 7 square degree sample of the deep Sloan Digital Sky Survey equatorial stripe (Stripe 82), from which we detect 97 clusters with z<=0.6. Benefiting from deeper data, we are 100% complete in the maxBCG optically-selected cluster catalogue (based on shallower single epoch SDSS data) and find an additional 78 previously unidentified clusters. The second dataset is a mock Medium Deep Survey (MDS) Pan-STARRS catalogue, based on the Lambda-CDM model and a semi-analytic galaxy formation recipe. Knowledge of galaxy-halo memberships in the mock allows a quantification of algorithm performance. We detect 305 mock clusters in haloes with mass >10^13 solar masses at z<=0.6 and determine a spurious detection rate of <1%, consistent with tests on the Stripe 82 catalogue. The detector performs well in the recovery of model Lambda-CDM clusters. (abridged)

Completeness - III. Identifying characteristic systematics and evolution in galaxy redshift surveys

This paper continues our development of non-parametric tests for analysing the completeness in apparent magnitude of magnitude-redshift surveys. The purpose of this third and final paper in our completeness series is two-fold: firstly we explore how certain forms of incompleteness for a given flux-limited galaxy redshift survey would manifest themselves in the ROBUST Tc and Tv completeness estimators introduced in our earlier papers; secondly we provide a comprehensive error propagation for these estimators. By using both real surveys and Monte Carlo mock survey data, we have found distinct, characteristic behaviour of the Tc and Tv estimators which identify incompleteness in the form of e.g. missing objects within a particular magnitude range. Conversely we have identified signatures of `over' completeness, in cases where a survey contains a small region in apparent magnitude that may have too many objects relative to the rest of the data set. We also demonstrate how incompleteness resulting from luminosity evolution can be identified and provide a framework for using our estimators as a robust tool for constraining models of luminosity evolution. Finally we explore the error propagation for Tc andTv. This builds on Completeness II by allowing the definition of these estimators, and their errors, via an adaptive procedure that accounts for the effects of sampling error on the observed distribution of apparent magnitude and redshift in a survey.

THE NEW HORIZON RUN COSMOLOGICAL N-BODY SIMULATIONS

We present two large cosmological N-body simulations, called Horizon Run 2 (HR2) and Horizon Run 3 (HR3), made using <TEX>$6000^3$</TEX> = 216 billions and <TEX>$7210^3$</TEX> = 374 billion particles, spanning a volume of <TEX>$(7.200\;h^{-1}Gpc)^3$</TEX> and <TEX>$(10.815\;h^{-1}Gpc)^3$</TEX>, respectively. These simulations improve on our previous Horizon Run 1 (HR1) up to a factor of 4.4 in volume, and range from 2600 to over 8800 times the volume of the Millennium Run. In addition, they achieve a considerably finer mass resolution, down to <TEX>$1.25{\times}10^{11}h^{-1}M_{\odot}$</TEX>, allowing to resolve galaxy-size halos with mean particle separations of <TEX>$1.2h^{-1}$</TEX>Mpc and <TEX>$1.5h^{-1}$</TEX>Mpc, respectively. We have measured the power spectrum, correlation function, mass function and basic halo properties with percent level accuracy, and verified that they correctly reproduce the CDM theoretical expectations, in excellent agreement with linear perturbation theory. Our unprecedentedly large-volume N-body simulations can be used for a variety of studies in cosmology and astrophysics, ranging from large-scale structure topology, baryon acoustic oscillations, dark energy and the characterization of the expansion history of the Universe, till galaxy formation science - in connection with the new SDSS-III. To this end, we made a total of 35 all-sky mock surveys along the past light cone out to z = 0.7 (8 from the HR2 and 27 from the HR3), to simulate the BOSS geometry. The simulations and mock surveys are already publicly available at http://astro.kias.re.kr/Horizon-Run23/.

Sweep widths and the detection of artifacts in archaeological survey

In many parts of the world, one of the principal means for discovering archaeological resources is terrestrial archaeological survey for small scatters of generally unobtrusive artifacts on the surface. Yet archaeologists have expended relatively little research on the factors that affect detection of such artifacts or the impacts they have on the reliability of surveys. We employ mock survey of plowed fields ‘seeded’ with a variety of artifacts in order to evaluate the effectiveness of pedestrian survey (fieldwalking) with respect to search time and transect spacing. Our results confirm theoretical expectations about the diminishing returns on increases of search effort, while also demonstrating variation in ‘sweep widths’ for different artifact types and surveyor speed and the effects of walking toward or away from the sun. Preliminary results have implications for the most efficient spacing of survey transects as well as the evaluation of completed surveys, since some artifact types have extremely low probabilities of detection even at high densities of search effort.

Simulating the effect of non-linear mode coupling in cosmological parameter estimation

Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naive Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2-D and tomographic shear analysis of a Euclid-like survey. In both cases we find that the 68% confidence area of the Omega_m-sigma_8 plane increases by a factor 5. However, the marginal errors increase by just 20 to 40%. We propose a new method to model the effects of nonlinear shear-power mode-coupling in the Fisher Matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68% confidence regions of the full Maximum Likelihood analysis in the Omega_m-sigma_8 plane to high accuracy for both 2-D and tomographic weak lensing surveys. Finally, we perform a multi-parameter analysis of Omega_m, sigma_8, h, n_s, w_0 and w_a to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. (Abridged)

Connected structure in the Two-degree Field Galaxy Redshift Survey

We describe and apply a simple prescription for defining connected structures in galaxy redshift surveys. The method is based upon two passes with a friends-of-friends groupfinder. The first pass uses a cylindrical linking volume to find galaxy groups and clusters, in order to suppress the line-of-sight smearing introduced by the large random velocities of galaxies within these deep potential wells. The second pass, performed with a spherical linking volume, identifies the connected components. This algorithm has been applied to the 2dFGRS, within which it picks out a total of 7,603 systems containing at least two galaxies and having a mean redshift less than 0.12. Connected systems with many members appear filamentary in nature, and the algorithm recovers two particularly large filaments within the 2dFGRS. For comparison, the algorithm is has also been applied to LambdaCDM mock galaxy surveys. While the model population of such systems is broadly similar to that in the 2dFGRS, it does not generally contain such extremely large structures.

Reevaluation of the PACU Patient Before Discharge

QUESTION: During a recent mock survey, the surveyors wanted to see documentation by an anesthesia provider that the patient had been reevaluated before discharge from the PACU. Is this different from the traditional “sign out” by anesthesia?

RECONSTRUCTING REDSHIFT DISTRIBUTIONS WITH CROSS-CORRELATIONS: TESTS AND AN OPTIMIZED RECIPE

Many of the cosmological tests to be performed by planned dark energy experiments will require extremely well-characterized photometric redshift measurements. Current estimates for cosmic shear are that the true mean redshift of the objects in each photo-z bin must be known to better than 0.002(1 + z), and the width of the bin must be known to ∼0.003(1 + z) if errors in cosmological measurements are not to be degraded significantly. A conventional approach is to calibrate these photometric redshifts with large sets of spectroscopic redshifts. However, at the depths probed by Stage III surveys (such as DES), let alone Stage IV (LSST, JDEM, and Euclid), existing large redshift samples have all been highly (25%–60%) incomplete, with a strong dependence of success rate on both redshift and galaxy properties. A powerful alternative approach is to exploit the clustering of galaxies to perform photometric redshift calibrations. Measuring the two-point angular cross-correlation between objects in some photometric redshift bin and objects with known spectroscopic redshift, as a function of the spectroscopic z, allows the true redshift distribution of a photometric sample to be reconstructed in detail, even if it includes objects too faint for spectroscopy or if spectroscopic samples are highly incomplete. We test this technique using mock DEEP2 Galaxy Redshift survey light cones constructed from the Millennium Simulation semi-analytic galaxy catalogs. From this realistic test, which incorporates the effects of galaxy bias evolution and cosmic variance, we find that the true redshift distribution of a photometric sample can, in fact, be determined accurately with cross-correlation techniques. We also compare the empirical error in the reconstruction of redshift distributions to previous analytic predictions, finding that additional components must be included in error budgets to match the simulation results. This extra error contribution is small for surveys that sample large areas of sky (>∼10°–100°), but dominant for ∼1 deg2 fields. We conclude by presenting a step-by-step, optimized recipe for reconstructing redshift distributions from cross-correlation information using standard correlation measurements.

THE HORIZON RUNN-BODY SIMULATION: BARYON ACOUSTIC OSCILLATIONS AND TOPOLOGY OF LARGE-SCALE STRUCTURE OF THE UNIVERSE

In support of the new Sloan III survey, which will measure the baryon oscillation scale using the luminous red galaxies (LRGs), we have run the largest N-body simulation to date using $4120^3 = 69.9$ billion particles, and covering a volume of $(6.592 h^{-1} {\rm Gpc})^3$. This is over 2000 times the volume of the Millennium Run, and corner-to-corner stretches all the way to the horizon of the visible universe. LRG galaxies are selected by finding the most massive gravitationally bound, cold dark matter subhalos, not subject to tidal disruption, a technique that correctly reproduces the 3D topology of the LRG galaxies in the Sloan Survey.We have measured the covariance function, power spectrum, and the 3D topology of the LRG galaxy distribution in our simulation and made 32 mock surveys along the past lightcone to simulate the Sloan III survey. Our large N-body simulation is used to accurately measure the non-linear systematic effects such as gravitational evolution, redshift space distortion, past light cone space gradient, and galaxy biasing, and to calibrate the baryon oscillation scale and the genus topology. For example, we predict from our mock surveys that the baryon acoustic oscillation peak scale can be measured with the cosmic variance-dominated uncertainty of about 5% when the SDSS-III sample is divided into three equal volume shells, or about 2.6% when a thicker shell with $0.4<z<0.6$ is used. We find that one needs to correct the scale for the systematic effects amounting up to 5.2% to use it to constrain the linear theories. And the uncertainty in the amplitude of the genus curve is expected to be about 1% at 15 $h^{-1}$Mpc scale. We are making the simulation and mock surveys publicly available.

The zCOSMOS survey. The dependence of clustering on luminosity and stellar mass at $z=0.2$–1

We study the dependence of galaxy clustering on luminosity and stellar mass at redshifts z ~ [0.2-1] using the first zCOSMOS 10K sample. We measure the redshift-space correlation functions xi(rp,pi) and its projection wp(rp) for sub-samples covering different luminosity, mass and redshift ranges. We quantify in detail the observational selection biases and we check our covariance and error estimate techniques using ensembles of semi-analytic mock catalogues. We finally compare our measurements to the cosmological model predictions from the mock surveys. At odds with other measurements, we find a weak dependence of galaxy clustering on luminosity in all redshift bins explored. A mild dependence on stellar mass is instead observed. At z~0.7, wp(rp) shows strong excess power on large scales. We interpret this as produced by large-scale structure dominating the survey volume and extending preferentially in direction perpendicular to the line-of-sight. We do not see any significant evolution with redshift of the amplitude of clustering for bright and/or massive galaxies. The clustering measured in the zCOSMOS data at 0.5<z<1 for galaxies with log(M/M_\odot)>=10 is only marginally consistent with predictions from the mock surveys. On scales larger than ~2 h^-1 Mpc, the observed clustering amplitude is compatible only with ~1% of the mocks. Thus, if the power spectrum of matter is LCDM with standard normalization and the bias has no unnatural scale-dependence, this result indicates that COSMOS has picked up a particularly rare, ~2-3 sigma positive fluctuation in a volume of ~10^6 h^-1 Mpc^3. These findings underline the need for larger surveys of the z~1 Universe to appropriately characterize the level of structure at this epoch.

ΛCDM predictions for galaxy protoclusters - I. The relation between galaxies, protoclusters and quasars at

Motivated by recent observational studies of the environment of z ∼ 6 QSOs, we have used the Millennium Run (MR) simulations to construct a very large (∼4° x 4°) mock redshift survey of star-forming galaxies at z ∼ 6. We use this simulated survey to study the relation between density enhancements in the distribution of i 775 -dropouts and Lya emitters, and their relation to the most massive haloes and protocluster regions at z ∼ 6. Our simulation predicts significant variations in surface density across the sky with some voids and filaments extending over scales of 1°, much larger than probed by current surveys. Approximately one-third of all z ∼ 6 haloes hosting i-dropouts brighter than z = 26.5 mag (≈M* UV,z=6 ) become part of z = 0 galaxy clusters.;-dropouts associated with protocluster regions are found in regions where the surface density is enhanced on scales ranging from a few to several tens of arcminutes on the sky. We analyse two structures of ('-dropouts and Lya emitters observed with the Subaru Telescope and show that these structures must be the seeds of massive clusters in formation. In striking contrast, six z ∼ 6 QSO fields observed with Hubble Space Telescope show no significant enhancements in their i 775 -dropout number counts. With the present data, we cannot rule out the QSOs being hosted by the most massive haloes. However, neither can we confirm this widely used assumption. We conclude by giving detailed recommendations for the interpretation and planning of observations by current and future ground- and space-based instruments that will shed new light on questions related to the large-scale structure at z ∼ 6.

Recovering the real-space correlation function from photometric redshift surveys

Measurements of clustering in large-scale imaging surveys that make use of photometric redshifts depend on the uncertainties in the redshift determination. We have used light-cone simulations to show how the deprojection method successfully recovers the real space correlation function when applied to mock photometric redshift surveys. We study how the errors in the redshift determination affect the quality of the recovered two-point correlation function. Considering the expected errors associated to the planned photometric redshift surveys, we conclude that this method provides information on the clustering of matter useful for the estimation of cosmological parameters that depend on the large scale distribution of galaxies.

Alignment between galaxies and large-scale structure

Based on the Sloan Digital Sky Survey DR6 (SDSS) and the Millennium Simulation (MS), we investigate the alignment between galaxies and large-scale structure. For this purpose, we develop two new statistical tools, namely the alignment correlation function and the cos(2θ)-statistic. The former is a two-dimensional extension of the traditional two-point correlation function and the latter is related to the ellipticity correlation function used for cosmic shear measurements. Both are based on the cross correlation between a sample of galaxies with orientations and a reference sample which represents the large-scale structure. We apply the new statistics to the SDSS galaxy catalog. The alignment correlation function reveals an overabundance of reference galaxies along the major axes of red, luminous (L ≲ L*) galaxies out to projected separations of 60 h-1 Mpc. The signal increases with central galaxy luminosity. No alignment signal is detected for blue galaxies. The cos(2θ)-statistic yields very similar results. Starting from a MS semi-analytic galaxy catalog, we assign an orientation to each red, luminous and central galaxy, based on that of the central region of the host halo (with size similar to that of the stellar galaxy). As an alternative, we use the orientation of the host halo itself. We find a mean projected misalignment between a halo and its central region of ∼ 25°. The misalignment decreases slightly with increasing luminosity of the central galaxy. Using the orientations and luminosities of the semi-analytic galaxies, we repeat our alignment analysis on mock surveys of the MS. Agreement with the SDSS results is good if the central orientations are used. Predictions using the halo orientations as proxies for central galaxy orientations overestimate the observed alignment by more than a factor of 2. Finally, the large volume of the MS allows us to generate a two-dimensional map of the alignment correlation function, which shows the reference galaxy distribution to be flattened parallel to the orientations of red luminous galaxies with axis ratios of ∼ 0.5 and ∼ 0.75 for halo and central orientations, respectively. These ratios are almost independent of scale out to 60 h-1 Mpc.

A calibration of the relation between the abundance of close galaxy pairs and the rate of galaxy mergers

Estimates of galaxy merger rates based on counts of close pairs typically assume that most of the observed systems will merge within a few hundred Myr (for projected pair separations ≤25 h−1kpc). Here we investigate these assumptions using virtual galaxy catalogues derived from the Millennium Simulation, a very large N-body simulation of structure formation in the concordance Λ cold dark matter (ΛCDM) cosmology. These catalogues have been shown to be at least roughly consistent with a wide range of properties of the observed galaxy population at both low and high redshift. Here we show that they also predict close pair abundances at low redshift which agree with those observed. They thus embed a realistic and realistically evolving galaxy population within the standard structure formation paradigm, and so are well suited to calibrate the relation between close galaxy pairs and mergers. We show that observational methods, when applied to our mock galaxy surveys, do indeed identify pairs which are physically close and due to merge. The sample-averaged merging time depends only weakly on the stellar mass and redshift of the pair. At z≤ 2 this time-scale is T≈T0r25M−0.3*, where r25 is the maximum projected separation of the pair sample in units of 25 h−1kpc, M* is the typical stellar mass of the pairs in units of 3 × 1010h−1M⊙ and the coefficient T0 is 1.1 Gyr for samples selected to have line-of-sight velocity difference smaller than 300 km s−1 and 1.6 Gyr for samples where this velocity difference is effectively unconstrained. These time-scales increase slightly with redshift and are longer than assumed in most observational studies, implying that merger rates have typically been overestimated.

The Clustering of SDSS Galaxy Groups: Mass and Color Dependence

We use a sample of galaxy groups selected from the SDSS DR 4 with an adaptive halo-based group finder to probe how the clustering strength of groups depends on their masses and colors. In particular, we determine the relative biases of groups of different masses, as well as that of groups with the same mass but with different colors. In agreement with previous studies, we find that more massive groups are more strongly clustered, and the inferred mass dependence of the halo bias is in good agreement with predictions for the $\Lambda$CDM cosmology. Regarding the color dependence, we find that groups with red centrals are more strongly clustered than groups of the same mass but with blue centrals. Similar results are obtained when the color of a group is defined to be the total color of its member galaxies. The color dependence is more prominent in less massive groups and becomes insignificant in groups with masses $\gta 10^{14}\msunh$. We construct a mock galaxy redshift survey constructed from the large Millenium simulation that is populated with galaxies according to the semi-analytical model of Croton et al. Applying our group finder to this mock survey, and analyzing the mock data in exactly the same way as the true data, we are able to accurately recover the intrinsic mass and color dependencies of the halo bias in the model. This suggests that our group finding algorithm and our method of assigning group masses do not induce spurious mass and/or color dependencies in the group-galaxy correlation function. The semi-analytical model reveals the same color dependence of the halo bias as we find in our group catalogue. In halos with $M\sim 10^{12}\msunh$, though, the strength of the color dependence is much stronger in the model than in the data.

On the accuracy of the high-redshift cluster luminosity function

We study the reliability of the statistical background subtraction method for computing the Ks-band luminosity function of cluster galaxies at z∼ 1 using mock Red-sequence Cluster Survey cluster catalogues constructed from galform semi-analytic galaxies. The underlying cluster luminosity function in the mocks is compatible with recent estimates at z∼ 1 by several authors. We simulate different samples where the number of clusters with Ks-band photometry goes from five to a maximum of 50, in order to find the most suitable observational sample to carry out this study; the current observational status in the near-infrared wavelength range has been reached using five real clusters at z∼ 1. We compute the composite luminosity function for several samples of galaxy clusters with masses ≃1.5 × 1014 M⊙ assuming a flux-limited, complete sample of galaxies down to Ks= 21.0 mag. We find that the Schechter fit parameters Ks* and α for a sample of galaxies with no redshift information are rather poorly constrained if both parameters are allowed to vary freely; if α is fixed at a fiducial value, then Ks* shows significantly improved stochastic uncertainties but can be influenced by systematic deviations. We find a significantly improved accuracy in the luminosity function parameters when adding photometric redshift information for bright cluster galaxies. The impact of a 10-fold increase in the number of clusters with available Ks-band photometry is that of decreasing stochastic errors in Ks* and α by factors of ≃2 and ≃4, respectively, for accuracies of up to (ΔKs*/Ks*)stochastic= 0.02 and (Δα/α)stochastic= 0.09. The dwarf-to-giant ratios inferred from the luminosity functions of red-sequence galaxies in the mock catalogue agree very well with the underlying values; however, there is an indication that the semi-analytic model overpredicts the abundance of dwarf galaxies by up to a factor of 3 with respect to recent measurements. Finally, we find that in order to use estimates of Ks* to study the formation redshift of cluster galaxies at z= 1, the sample would need to contain 520 z∼ 1 clusters, for an accuracy of ∼2 Gyr at the 68 per cent confidence level. However, combining this method with other estimates may significantly reduce the sample size, and allow important new constraints on galaxy formation models.