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We use three semi-analytical models (SAMs) of galaxy formation and evolution run on the same 1  h −1 Gpc MultiDark Planck2 cosmological simulation to investigate the properties of [O  ii ] emission line galaxies at redshift z ∼ 1. We compare model predictions with different observational data sets, including DEEP2– firefly galaxies with absolute magnitudes. We estimate the [O  ii ] luminosity (⁠|$L{\left[\rm{O\,{\small II}}\right]}$|⁠) of our model galaxies using the public code get_ emlines  , which ideally assumes as input the instantaneous star formation rates (SFRs). This property is only available in one of the SAMs under consideration, while the others provide average SFRs, as most models do. We study the feasibility of inferring galaxies'    |$L{\left[\rm{O\,{\small II}}\right]}$|   from average SFRs in post-processing. We find that the result is accurate for model galaxies with dust attenuated   |$L{\left[\rm{O\,{\small II}}\right]}$|  ≲ 1042.2 erg s−1 (⁠|$\lt 5{{\ \rm per\ cent}}$| discrepancy). The galaxy properties that correlate the most with the model   |$L{\left[\rm{O\,{\small II}}\right]}$|  are the SFR and the observed-frame u and g broad-band magnitudes. Such correlations have r -values above 0.64 and a dispersion that varies with   |$L{\left[\rm{O\,{\small II}}\right]}$|  . We fit these correlations with simple linear relations and use them as proxies for   |$L{\left[\rm{O\,{\small II}}\right]}$|  , together with an observational conversion that depends on SFR and metallicity. These proxies result in [O  ii ] luminosity functions and halo occupation distributions with shapes that vary depending on both the model and the method used to derive   |$L{\left[\rm{O\,{\small II}}\right]}$|  . The amplitude of the clustering of model galaxies with   |$L{\left[\rm{O\,{\small II}}\right]}$|  >1040.4 erg s−1 remains overall unchanged on scales above 1  |$\, h^{-1}$|  Mpc, independently of the |$L{\left[\rm{O\,{\small II}}\right]}$| computation. [ABSTRACT FROM AUTHOR]

The primary difficulty in measuring dynamical masses of galaxy clusters from galaxy data lies in the separation between true cluster members from interloping galaxies along the line of sight. We study the impact of membership contamination and incompleteness on cluster mass estimates obtained with 25 commonly used techniques applied to nearly 1000 mock clusters with precise spectroscopic redshifts. We show that all methods overestimate or underestimate cluster masses when applied to contaminated or incomplete galaxy samples, respectively. This appears to be the main source of the intrinsic scatter in the mass scaling relation. Applying corrections based on a prior knowledge of contamination and incompleteness can reduce the scatter to the level of shot noise expected for poorly sampled clusters. We establish an empirical model quantifying the effect of imperfect membership on cluster mass estimation and discuss its universal and method-dependent features. We find that both imperfect membership and the response of the mass estimators depend on cluster mass, effectively causing a flattening of the estimated–true mass relation. Imperfect membership thus alters cluster counts determined from spectroscopic surveys, hence the cosmological parameters that depend on such counts. [ABSTRACT FROM AUTHOR]

With the advent of wide-field cosmological surveys, we are approaching samples of hundreds of thousands of galaxy clusters. While such large numbers will help reduce statistical uncertainties, the control of systematics in cluster masses is crucial. Here we examine the effects of an important source of systematic uncertainty in galaxy-based cluster mass estimation techniques: the presence of significant dynamical substructure. Dynamical substructure manifests as dynamically distinct subgroups in phase-space, indicating an 'unrelaxed' state. This issue affects around a quarter of clusters in a generally selected sample. We employ a set of mock clusters whose masses have been measured homogeneously with commonly used galaxy-based mass estimation techniques (kinematic, richness, caustic, radial methods). We use these to study how the relation between observationally estimated and true cluster mass depends on the presence of substructure, as identified by various popular diagnostics.We find that the scatter for an ensemble of clusters does not increase dramatically for clusters with dynamical substructure. However, we find a systematic bias for all methods, such that clusters with significant substructure have higher measured masses than their relaxed counterparts. This bias depends on cluster mass: the most massive clusters are largely unaffected by the presence of significant substructure, but masses are significantly overestimated for lower mass clusters, by ~10 per cent at 1014 and ≳20 per cent for ≲1013.5. The use of cluster samples with different levels of substructure can therefore bias certain cosmological parameters up to a level comparable to the typical uncertainties in current cosmological studies. [ABSTRACT FROM AUTHOR]

This paper is the second in a series in which we perform an extensive comparison of various galaxy-based cluster mass estimation techniques that utilize 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 (0.18-1.08 dex, i.e. a factor of ~1.5-12), 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 overestimated 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 utilize the masses, richnesses, or abundances of clusters, which have different uncertainties when different methods are used. [ABSTRACT FROM AUTHOR]

ABSTRACT For galaxy clustering to provide robust constraints on cosmological parameters and galaxy formation models, it is essential to make reliable estimates of the errors on clustering measurements. We present a new technique, based on a spatial jackknife (JK) resampling, which provides an objective way to estimate errors on clustering statistics. Our approach allows us to set the appropriate size for the JK subsamples. The method also provides a means to assess the impact of individual regions on the measured clustering, and thereby to establish whether or not a given galaxy catalogue is dominated by one or several large structures, preventing it to be considered as a 'fair sample'. We apply this methodology to the two- and three-point correlation functions measured from a volume-limited sample of M* galaxies drawn from Data Release 7 of the Sloan Digital Sky Survey (SDSS). The frequency of JK subsample outliers in the data is shown to be consistent with that seen in large N-body simulations of clustering in the cosmological constant plus cold dark matter cosmology. We also present a comparison of the three-point correlation function in SDSS and Two-degree-Field Galaxy Redshift Survey using this approach and find consistent measurements between the two samples. [ABSTRACT FROM AUTHOR]

We present a test of different error estimators for two-point clustering statistics, appropriate for present and future large galaxy redshift surveys. Using an ensemble of very large dark matter ΛCDM N-body simulations, we compare internal error estimators (jackknife and bootstrap) to external ones (Monte Carlo realizations). For three-dimensional clustering statistics, we find that none of the internal error methods investigated is able to reproduce either accurately or robustly the errors of external estimators on 1 to scales. The standard bootstrap overestimates the variance of by ∼40 per cent on all scales probed, but recovers, in a robust fashion, the principal eigenvectors of the underlying covariance matrix. The jackknife returns the correct variance on large scales, but significantly overestimates it on smaller scales. This scale dependence in the jackknife affects the recovered eigenvectors, which tend to disagree on small scales with the external estimates. Our results have important implications for fitting models to galaxy clustering measurements. For example, in a two-parameter fit to the projected correlation function, we find that the standard bootstrap systematically overestimates the 95 per cent confidence interval, while the jackknife method remains biased, but to a lesser extent. Ignoring the systematic bias, the scatter between realizations, for Gaussian statistics, implies that a 2σ confidence interval, as inferred from an internal estimator, corresponds in practice to anything from 1σ to 3σ. By oversampling the subvolumes, we find that it is possible, at least for the cases we consider, to obtain robust bootstrap variances and confidence intervals that agree with external error estimates. Our results are applicable to two-point statistics, like and , measured in large redshift surveys, and show that the interpretation of clustering measurements with internally estimated errors should be treated with caution. [ABSTRACT FROM AUTHOR]

We investigate halo mass selection properties of red-sequence cluster finders using galaxy populations of the Millennium Simulation (MS). A clear red sequence exists for MS galaxies in massive haloes at redshifts z < 1, and we use this knowledge to inform a cluster-finding algorithm applied to 500 h−1 Mpc projections of the simulated volume. At low redshift , we find that 90 per cent of the clusters found have galaxy membership dominated by a single, real-space halo, and that 10 per cent are blended systems for which no single halo contributes a majority of a cluster's membership. At , the fraction of blends increases to 22 per cent, as weaker redshift evolution in observed colour extends the comoving length probed by a fixed range of colour. Other factors contributing to the increased blending at high z include broadening of the red sequence and confusion from a larger number of intermediate-mass haloes hosting bright red galaxies of magnitude similar to those in higher mass haloes. Our method produces catalogues of cluster candidates whose halo mass selection function, p( M| Ngal, z), is characterized by a bimodal lognormal model with a dominant component that reproduces well the real-space distribution, and a redshift-dependent tail that is broader and displaced by a factor of ∼2 lower in mass. We discuss implications for X-ray properties of optically selected clusters and offer ideas for improving both mock catalogues and cluster finding in future surveys. [ABSTRACT FROM AUTHOR]

We present new results for the three-point correlation function, ζ, measured as a function of scale, luminosity and colour from the final version of the 2dF Galaxy Redshift Survey (2dFGRS). The reduced three-point correlation function, , is estimated for different triangle shapes and sizes, employing a full covariance analysis. The form of Q3 is consistent with the expectations for the Λ cold dark matter model, confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on Gaussian primordial fluctuations. However, we find a clear offset in amplitude between Q3 for galaxies and the predictions for the dark matter. We are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9σ level. On weakly non-linear scales, we can interpret our results in terms of galaxy bias parameters. We find a linear bias term that is consistent with unity, and a quadratic bias . This is the first significant detection of a non-zero quadratic bias, indicating a small but important non-gravitational contribution to the three-point function. Our estimate of the linear bias from the three-point function is independent of the normalization of underlying density fluctuations, so we can combine this with the measurement of the power spectrum of 2dFGRS galaxies to constrain the amplitude of matter fluctuations. We find that the rms linear theory variance in spheres of radius Mpc is , providing an independent confirmation of values derived from other techniques. On non-linear scales, where , we find that Q3 has a strong dependence on scale, colour and luminosity. [ABSTRACT FROM AUTHOR]

We measure moments of the galaxy count probability distribution function in the Two-degree Field Galaxy Redshift Survey (2dFGRS). The survey is divided into volume-limited subsamples in order to examine the dependence of the higher-order clustering on galaxy luminosity. We demonstrate the hierarchical scaling of the averaged p-point galaxy correlation functions, [This equation cannot be represented into ASCII Text] up to p = 6. The hierarchical amplitudes, [This equation cannot be represented into ASCII Text] are approximately independent of the cell radius used to smooth the galaxy distribution on small to medium scales. On larger scales we find that the higher-order moments can be strongly affected by the presence of rare, massive superstructures in the galaxy distribution. The skewness S3 has a weak dependence on luminosity, approximated by a linear dependence on log luminosity. We discuss the implications of our results for simple models of linear and non-linear bias that relate the galaxy distribution to the underlying mass. [ABSTRACT FROM AUTHOR]

We use the Two-Degree Field Galaxy Redshift Survey (2dFGRS) to test the hierarchical scaling hypothesis: namely, that the p-point galaxy correlation functions can be written in terms of the two-point correlation function or variance. This scaling is expected if an initially Gaussian distribution of density fluctuations evolves under the action of gravitational instability. We measure the volume-averaged p-point correlation functions using a counts-in-cells technique applied to a volume-limited sample of 44 931 L* galaxies. We demonstrate that L* galaxies display hierarchical clustering up to order in redshift space. The variance measured for L* galaxies is in excellent agreement with the predictions from a Λ-cold dark matter N-body simulation. This applies to all cell radii considered, . However, the higher order correlation functions of L* galaxies have a significantly smaller amplitude than is predicted for the dark matter for . This disagreement implies that a non-linear bias exists between the dark matter and L* galaxies on these scales. We also show that the presence of two rare, massive superclusters in the 2dFGRS has an impact on the higher-order clustering moments measured on large scales. [ABSTRACT FROM AUTHOR]