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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.

This paper is the first 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 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 idealized 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 R₂₀₀, with no substructure nor colour segregation, and with isotropic, isothermal Maxwellian velocities. We find that, above 1014Mʘ, recovered cluster masses are correlated with the true underlying cluster mass with an intrinsic scatter of typically a factor of 2. Below 1014Mʘ, 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.

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 > or ~20 per cent for < or ~ 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.

We present a comparison of 14 galaxy formation models: 12 different semi-analytical models and 2 halo occupation distribution models for galaxy formation based upon the same cosmological simulation and merger tree information derived from it. The participating codes have proven to be very successful in their own right but they have all been calibrated independently using various observational data sets, stellar models, and merger trees. In this paper, we apply them without recalibration and this leads to a wide variety of predictions for the stellar mass function, specific star formation rates, stellar-to-halo mass ratios, and the abundance of orphan galaxies. The scatter is much larger than seen in previous comparison studies primarily because the codes have been used outside of their native environment within which they are well tested and calibrated. The purpose of the ‘nIFTy comparison of galaxy formation models’ is to bring together as many different galaxy formation modellers as possible and to investigate a common approach to model calibration. This paper provides a unified description for all participating models and presents the initial, uncalibrated comparison as a baseline for our future studies where we will develop a common calibration framework and address the extent to which that reduces the scatter in the model predictions seen here.