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Register a new userGalaxy Cluster Mass Reconstruction Project: II. Quantifying scatter and bias using contrasting mock catalogues
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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.
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We describe the construction of a suite of galaxy cluster mock catalogues from N-body simulations, based on the properties of the new ROSAT-ESO Flux-Limited X-Ray (REFLEX II) galaxy cluster catalogue. Our procedure is based on the measurements of the cluster abundance, and involves the calibration of the underlying scaling relation linking the mass of dark matter haloes to the cluster X-ray luminosity determined in the emph{ROSAT} energy band $0.1-2.4$ keV. In order to reproduce the observed abundance in the luminosity range probed by the REFLEX II X-ray luminosity function ($0.01<L_{X}/(10^{44}{rm erg},{rm s}^{-1}h^{-2})<10$), a mass-X ray luminosity relation deviating from a simple power law is required. We discuss the dependence of the calibration of this scaling relation on the X-ray luminosity and the definition of halo masses and analyse the one- and two-point statistical properties of the mock catalogues. Our set of mock catalogues provides samples with self-calibrated scaling relations of galaxy clusters together with inherent properties of flux-limited surveys. This makes them a useful tool to explore different systematic effects and statistical methods involved in constraining both astrophysical and cosmological information from present and future galaxy cluster surveys.
(Abridged) We quantify the bias and scatter in galaxy cluster masses and concentrations derived from an idealised mock weak gravitational lensing (WL) survey, and their effect on the cluster mass-concentration relation. For this, we simulate WL distortions on a population of background galaxies due to a large (~3000) sample of galaxy cluster haloes extracted from the Millennium Simulation at z~0.2. This study takes into account the influence of shape noise, cluster substructure and asphericity as well as correlated large-scale structure, but not uncorrelated large-scale structure along the line of sight and observational effects. We find a small, but non-negligble, negative median bias in both mass and concentration at a level of ~5%, the exact value depending both on cluster mass and radial survey range. Both the mass and concentration derived from WL show considerable scatter about their true values. This scatter has, even for the highest mass clusters of M200 > 10^14.8 M_sun, a level of ~30% and ~20% for concentration and mass respectively and increases strongly with decreasing cluster mass. For a typical survey analysing 30 galaxies per arcmin^2 over a radial range from 30 to 15 from the cluster centre, the derived M200-c relation has a slope and normalisation too low compared to the underlying true (3D) relation by ~40% and ~15% respectively. The scatter and bias in mass are shown to reflect a departure at large radii of the true WL shear/matter distribution of the simulated clusters from the NFW profile adopted in modelling the mock observations. Orientation of the triaxial cluster haloes dominates the concentration scatter (except at low masses, where galaxy shape noise becomes dominant), while the bias in c is mostly due to substructure within the virial radius.
This paper is the first 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 primary aim is to test the performance of these cluster mass estimation techniques on a diverse set of models that will increase in complexity. We begin by providing participating methods with data from a simple model that delivers idealised clusters, enabling us to quantify the underlying scatter intrinsic to these mass estimation techniques. The mock catalogue is based on a Halo Occupation Distribution (HOD) model that assumes spherical Navarro, Frenk and White (NFW) haloes truncated at R_200, with no substructure nor colour segregation, and with isotropic, isothermal Maxwellian velocities. We find that, above 10^14 M_solar, recovered cluster masses are correlated with the true underlying cluster mass with an intrinsic scatter of typically a factor of two. Below 10^14 M_solar, the scatter rises as the number of member galaxies drops and rapidly approaches an order of magnitude. We find that richness-based methods deliver the lowest scatter, but it is not clear whether such accuracy may simply be the result of using an over-simplistic model to populate the galaxies in their haloes. Even when given the true cluster membership, large scatter is observed for the majority non-richness-based approaches, suggesting that mass reconstruction with a low number of dynamical tracers is inherently problematic.
Cosmological inference from cluster number counts is systematically limited by the accuracy of the mass calibration, i.e. the empirical determination of the mapping between cluster selection observables and halo mass. In this work we demonstrate a method to quantitatively determine the bias and uncertainties in weak-lensing mass calibration. To this end, we extract a library of projected matter density profiles from hydrodynamical simulations. Accounting for shear bias and noise, photometric redshift uncertainties, mis-centering, cluster member contamination, cluster morphological diversity, and line-of-sight projections, we produce a library of shear profiles. Fitting a one-parameter model to these profiles, we extract the so-called emph{weak lensing mass} $M_text{WL}$. Relating the weak-lensing mass to the halo mass from gravity-only simulations with the same initial conditions as the hydrodynamical simulations allows us to estimate the impact of hydrodynamical effects on cluster number counts experiments. Creating new shear libraries for $sim$1000 different realizations of the systematics, provides a distribution of the parameters of the weak-lensing to halo mass relation, reflecting their systematic uncertainty. This result can be used as a prior for cosmological inference. We also discuss the impact of the inner fitting radius on the accuracy, and determine the outer fitting radius necessary to exclude the signal from neighboring structures. Our method is currently being applied to different Stage~III lensing surveys, and can easily be extended to Stage~IV lensing surveys.
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 becomes ever more 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 $sim10%$ at $10^{14}$ and $geq20%$ for $leq10^{13.5}$. 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.
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