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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.

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.

JWST was conceived and built to answer one of the most fundamental questions that humans can address empirically: "How did the Universe make its first stars?". Our First Lights At REionization (FLARE) project transforms the quest for the epoch of reionization from the static to the time domain. It targets the complementary question: "What happened to those first stars?". It will be answered by observations of the most luminous events: supernovae and accretion on to black holes formed by direct collapse from the primordial gas clouds. These transients provide direct constraints on star-formation rates (SFRs) and the truly initial Initial Mass Function (IMF), and they may identify possible stellar seeds of supermassive black holes (SMBHs). Furthermore, our knowledge of the physics of these events at ultra-low metallicity will be much expanded. JWST's unique capabilities will detect these most luminous and earliest cosmic messengers easily in fairly shallow observations. However, these events are very rare at the dawn of cosmic structure formation and so require large area coverage. Time domain astronomy can be advanced to an unprecedented depth by means of a shallow field of JWST reaching 27 mag AB in 2 and 4.4 microns over a field as large as 0.1 square degree visited multiple times each year. Such a survey may set strong constraints or detect massive Pop III SNe at redshifts beyond 10, pinpointing the redshift of the first stars, or at least their death. Based on our current knowledge of superluminous supernovae (SLSNe), such a survey will find one or more SLSNe at redshifts above 6 in five years and possibly several direct collapse black holes. Although JWST is not designed as a wide field survey telescope, we show that such a wide field survey is possible with JWST and is critical in addressing several of its key scientific goals.

The velocity function is a fundamental observable statistic of the galaxy population, similarly impor- tant as the luminosity function, but much more difficult to measure. In this work we present the first directly measured circular velocity function that is representative between 60 < v_circ < 320 km/s for galaxies of all morphological types at a given rotation velocity. For the low mass galaxy population (60 < v_circ < 170 km/s), we use the HIPASS velocity function. For the massive galaxy population (170 < v_circ < 320 km/s), we use stellar circular velocities from the Calar Alto Legacy Integral Field Area Survey (CALIFA). In earlier work we obtained the measurements of circular velocity at the 80% light radius for 226 galaxies and demonstrated that the CALIFA sample can produce volume- corrected galaxy distribution functions. The CALIFA velocity function includes homogeneous velocity measurements of both late and early-type rotation-supported galaxies and has the crucial advantage of not missing gas-poor massive ellipticals that HI surveys are blind to. We show that both velocity functions can be combined in a seamless manner, as their ranges of validity overlap. The resulting observed velocity function is compared to velocity functions derived from cosmological simulations of the z = 0 galaxy population. We find that dark matter-only simulations show a strong mismatch with the observed VF. Hydrodynamic simulations fare better, but still do not fully reproduce observations., Accepted to ApJL. Keywords: Galaxies: kinematics and dynamics - galaxies: statistics - galaxies: evolution 7 pages, 3 figures

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.

As synoptic all-sky surveys begin to discover new multiply lensed quasars, the flow of data will enable statistical cosmological microlensing studies of sufficient size to constrain quasar accretion disc and supermassive black hole properties. In preparation for this new era, we are undertaking the GPU-Enabled, High Resolution cosmological MicroLensing parameter survey (GERLUMPH). We present here the GERLUMPH Data Release 1, which consists of 12342 high resolution cosmological microlensing magnification maps and provides the first uniform coverage of the convergence, shear and smooth matter fraction parameter space. We use these maps to perform a comprehensive numerical investigation of the mass-sheet degeneracy, finding excellent agreement with its predictions. We study the effect of smooth matter on microlensing induced magnification fluctuations. In particular, in the minima and saddle-point regions, fluctuations are enhanced only along the critical line, while in the maxima region they are always enhanced for high smooth matter fractions (~0.9). We describe our approach to data management, including the use of an SQL database with a Web interface for data access and online analysis, obviating the need for individuals to download large volumes of data. In combination with existing observational databases and online applications, the GERLUMPH archive represents a fundamental component of a new microlensing eResearch cloud. Our maps and tools are publicly available at http://gerlumph.swin.edu.au/., Comment: 9 pages, 9 figures, 2 tables, accepted for publication in ApJ

We have used high-resolution, HST WFC3/IR, near-infrared imaging to conduct a detailed bulge-disk decomposition of the morphologies of ~200 of the most massive (M_star > 10^11 M_solar) galaxies at 12 they are mostly disk-dominated. Interestingly, we find that while most of the quiescent galaxies are bulge-dominated, a significant fraction (25-40%) of the most quiescent galaxies, have disk-dominated morphologies. Thus, our results suggest that the physical mechanisms which quench star-formation activity are not simply connected to those responsible for the morphological transformation of massive galaxies., Contributed article (4 pages, 2 figures), IAU Symposium 295 on "The intriguing life of massive galaxies", to appear in the proceedings of the IAU XXVIII General Assembly, Beijing, 2012, (Eds: Daniel Thomas, Anna Pasquali, Ignacio Ferreras)

We have used deep, HST, near-IR imaging to study the morphological properties of the most massive galaxies at high z, modelling the WFC3/IR H-band images of the ~200 galaxies in the CANDELS-UDS field with 1 < z_phot < 3, and stellar masses M_star > 10^11 M_sun. We have used both single-Sersic and bulge+disk models, have investigated the errors/biases introduced by uncertainties in the background and the PSF, and have obtained formally-acceptable model fits to >90% of the galaxies. Our results indicate that these massive galaxies at 1 < z < 3 lie both on and below the local size-mass relation, with a median R_e~2.6 kpc, a factor of ~2.3 smaller than comparably-massive local galaxies. Moreover, we find that bulge-dominated objects in particular show evidence for a growing bimodality in the size-mass relation with increasing z, and by z > 2 the compact bulges display effective radii a factor ~4 smaller than local ellipticals of comparable mass. These trends appear to extend to the bulge components of disk-dominated galaxies, and vice versa. We also find that, while such massive galaxies at low z are bulge-dominated, at 1 < z < 2 they are predominantly mixed bulge+disk systems, and by z > 2 they are mostly disk-dominated. The majority of the disk-dominated galaxies are actively forming stars, but this is also true for many of the bulge-dominated systems. Interestingly, however, while most of the quiescent galaxies are bulge-dominated, we find that a significant fraction (25-40%) of the most quiescent galaxies have disk-dominated morphologies. Thus, while our results show that the massive galaxy population is undergoing dramatic changes at this crucial epoch, they also suggest that the physical mechanisms which quench star-formation activity are not simply connected to those responsible for the morphological transformation of massive galaxies into present-day giant ellipticals., 39 pages, 19 figures, 2 tables, submitted to MNRAS

We have used deep, HST, near-IR imaging to study the morphological properties of the most massive galaxies at high z, modelling the WFC3/IR H-band images of the ~200 galaxies in the CANDELS-UDS field with 1 < z_phot < 3, and stellar masses M_star > 10^11 M_sun. We have used both single-Sersic and bulge+disk models, have investigated the errors/biases introduced by uncertainties in the background and the PSF, and have obtained formally-acceptable model fits to >90% of the galaxies. Our results indicate that these massive galaxies at 1 < z < 3 lie both on and below the local size-mass relation, with a median R_e~2.6 kpc, a factor of ~2.3 smaller than comparably-massive local galaxies. Moreover, we find that bulge-dominated objects in particular show evidence for a growing bimodality in the size-mass relation with increasing z, and by z > 2 the compact bulges display effective radii a factor ~4 smaller than local ellipticals of comparable mass. These trends appear to extend to the bulge components of disk-dominated galaxies, and vice versa. We also find that, while such massive galaxies at low z are bulge-dominated, at 1 < z < 2 they are predominantly mixed bulge+disk systems, and by z > 2 they are mostly disk-dominated. The majority of the disk-dominated galaxies are actively forming stars, but this is also true for many of the bulge-dominated systems. Interestingly, however, while most of the quiescent galaxies are bulge-dominated, we find that a significant fraction (25-40%) of the most quiescent galaxies have disk-dominated morphologies. Thus, while our results show that the massive galaxy population is undergoing dramatic changes at this crucial epoch, they also suggest that the physical mechanisms which quench star-formation activity are not simply connected to those responsible for the morphological transformation of massive galaxies into present-day giant ellipticals., Comment: 39 pages, 19 figures, 2 tables, submitted to MNRAS

Recent low-redshift observations have attempted to determine the star formation histories of elliptical galaxies by tracking correlations between the stellar population parameters (age and metallicity) and the structural parameters that enter the fundamental plane (size and velocity dispersion). These studies have found that velocity dispersion, rather than effective radius or dynamical mass, is the main predictor of a galaxy's stellar age and metallicity. In this work, we apply an analytic model that predicts the structural properties of remnants formed in major mergers to progenitor disk galaxies with properties taken from two different semi-analytic models. We predict the effective radius, velocity dispersion, luminosity, age, and metallicity of the merger remnants, enabling us to compare directly to observations of early-type galaxies. While we find a tight correlation between age and velocity dispersion, we find a stronger dependence of age and metallicity on effective radius than observations report. The correlations arise as a result of the dependence of gas fraction, age, and metallicity on the stellar mass in the progenitor disk galaxies. These dependences induce a rotation in the radius-velocity plane between the correlations with effective radius and circular velocity in the disk galaxy progenitors, and the correlations with effective radius and velocity dispersion in the elliptical galaxy remnants. The differences between our results and those from observations suggest that major mergers alone cannot produce the observed lack of correlation between effective radius and stellar population parameters. Simulations have suggested that subsequent minor mergers introduce scatter in the effective radius while leaving the velocity dispersion essentially unchanged. Incorporating such minor mergers into the model may, then, bring the simulations into closer agreement with observations., 20 pages, 17 figures. Submitted to MNRAS

There are strong correlations between the three structural properties of elliptical galaxies -- stellar mass, velocity dispersion and size -- in the form of a tight "fundamental plane" and a "scaling relation" between each pair. Major mergers of disk galaxies are assumed to be a mechanism for producing ellipticals, but semi-analytic galaxy formation models (SAM) have encountered apparent difficulties in reproducing the observed slope and scatter of the size-mass relation. We study the scaling relations of merger remnants using progenitor properties from two SAMs. We apply a simple merger model that includes gas dissipation and star formation based on theoretical considerations and simulations. Combining the SAMs and the merger model allows calculation of the structural properties of the remnants of major mergers that enter the population of elliptical galaxies at a given redshift. Without tuning the merger model parameters for each SAM, the results roughly match the slope and scatter in the observed scaling relations and their evolution in the redshift range $z=0-3$. Within this model, the observed scaling relations, including the tilt of the fundamental plane relative to the virial plane, result primarily from the decrease of gas fraction with increasing progenitor mass. The scatter in the size-mass relation of the remnants is reduced from that of the progenitors because of a correlation between progenitor size and gas fraction at a given mass., in press

One of the main themes in extragalactic astronomy for the next decade will be the evolution of galaxies over cosmic time. Many future observatories, including JWST, ALMA, GMT, TMT and E-ELT will intensively observe starlight over a broad redshift range, out to the dawn of the modern Universe when the first galaxies formed. It has, however, become clear that the properties and evolution of galaxies are intimately linked to the growth of their central black holes. Understanding the formation of galaxies, and their subsequent evolution, will therefore be incomplete without similarly intensive observations of the accretion light from supermassive black holes (SMBH) in galactic nuclei. To make further progress, we need to chart the formation of typical SMBH at z>6, and their subsequent growth over cosmic time, which is most effectively achieved with X-ray observations. Recent technological developments in X-ray optics and instrumentation now bring this within our grasp, enabling capabilities fully matched to those expected from flagship observatories at longer wavelengths., 8 pages, Science White paper submitted to Astro2010 Decadal survey. Supplementary information available at http://astro.imperial.ac.uk/research/ixo/smbh_growth.shtml

We discuss the relationship between rest-frame color and optical luminosity for X-ray sources in the range 0.6, Comment: 5 pages, 2 figures, accepted for publication in AEGIS ApJ Letters special edition

We present new results for the 3-point correlation function, \zeta, measured as a function of scale, luminosity and colour from the final version of the two-degree field galaxy redshift survey (2dFGRS). The reduced three point correlation function, Q_3 is estimated for different triangle shapes and sizes, employing a full covariance analysis. The form of Q_3 is consistent with the expectations for the \Lambda-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 Q_3 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 9-sigma 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, b_1 = 0.93^{+0.10}_{-0.08} and a quadratic bias c_2 = b_2 /b_1 = -0.34^{+0.11}_{-0.08}. 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 normalisation 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 8Mpc/h is \sigma_8 = 0.88^{+0.12}_{-0.10}, providing an independent confirmation of values derived from other techniques. On non-linear scales, where \xi>1, we find that Q_3 has a strong dependence on scale, colour and luminosity., Comment: 16 pages, 10 figures, minor changes, extended comparison to previous results, accepted for publication in MNRAS

We have used high-resolution, HST WFC3/IR, near-infrared imaging to conduct a detailed bulge-disk decomposition of the morphologies of ~200 of the most massive (M_star > 10^11 M_solar) galaxies at 12 they are mostly disk-dominated. Interestingly, we find that while most of the quiescent galaxies are bulge-dominated, a significant fraction (25-40%) of the most quiescent galaxies, have disk-dominated morphologies. Thus, our results suggest that the physical mechanisms which quench star-formation activity are not simply connected to those responsible for the morphological transformation of massive galaxies., Comment: Contributed article (4 pages, 2 figures), IAU Symposium 295 on "The intriguing life of massive galaxies", to appear in the proceedings of the IAU XXVIII General Assembly, Beijing, 2012, (Eds: Daniel Thomas, Anna Pasquali, Ignacio Ferreras)

We introduce the Uchuu suite of large high-resolution cosmological N-body simulations. The largest simulation, named Uchuu, consists of 2.1 trillion (12 8003) dark matter particles in a box of side-length 2.0 h-1, Gpc$, with particle mass of 3.27 × 108, h-1, M⊙. The highest resolution simulation, Shin-Uchuu, consists of 262 billion (64003) particles in a box of side-length 140 h-1, Mpc, with particle mass of 8.97 × 105, h-1, M⊙. Combining these simulations, we can follow the evolution of dark matter haloes and subhaloes spanning those hosting dwarf galaxies to massive galaxy clusters across an unprecedented volume. In this first paper, we present basic statistics, dark matter power spectra, and the halo and subhalo mass functions, which demonstrate the wide dynamic range and superb statistics of the Uchuu suite. From an analysis of the evolution of the power spectra, we conclude that our simulations remain accurate from the baryon acoustic oscillation scale down to the very small. We also provide parameters of a mass-concentration model, which describes the evolution of halo concentration and reproduces our simulation data to within 5 per cent for haloes with masses spanning nearly eight orders of magnitude at redshift 0 ≤ z ≤ 14. There is an upturn in the mass-concentration relation for the population of all haloes and of relaxed haloes at z ≳ 0.5, whereas no upturn is detected at z < 0.5. We make publicly available various N-body products as part of Uchuu Data Release 1 on the Skies & Universes site. Future releases will include gravitational lensing maps and mock galaxy, X-ray cluster, and active galactic nucleus catalogues. © 2021 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society., The Uchuu simulations were carried out on Aterui II supercomputer at Center for Computational Astrophysics, CfCA, of National Astronomical Observatory of Japan, and the K computer at the RIKEN Advanced Institute for Computational Science (Proposal numbers hp180180, hp190161). The Uchuu DR1 effort has made use of the skun6@IAA facility managed by the IAA-CSIC in Spain, this equipment was funded by the Spanish MICINN EU-FEDER infrastructure grant EQC2018-004366-P. The skun@IAA_RedIRIS server was funded by the MICINN grant AYA2014-60641-C2-1-P. The numerical analysis was partially carried out on XC40 at the Yukawa Institute Computer Facility in Kyoto University. TI has been supported by MEXT via the ‘Priority Issue on Post-K computer’ (Elucidation of the Fundamental Laws and Evolution of the Universe), JICFUS, and MEXT via the ‘Program for Promoting Researches on the Supercomputer Fugaku’ (Toward a unified view of the universe: from large scale structures to planets, proposal numbers hp200124). TI thanks the support by MEXT/JSPS KAKENHI Grant Numbers JP17H04828, JP18H04337, JP19KK0344, and JP20H05245. FP, AK, and DM thank the support of the Spanish Ministry of Science and Innovation funding grant PGC2018-101931-B-I00. Parts of this research were conducted under the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. EJ acknowledges financial support from CNRS. FP and EJ want to thank a French–Spanish international collaboration grant from CNRS and CSIC. CVM acknowledges support from FONDECYT through grant 3200918, and he also acknowledges previous support from the Max Planck Society through a Partner Group grant. SAC acknowledges funding from Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET, PIP-0387), Agencia Nacional de Promoción de la Investigación, el Desarrollo Tecnológico y la Innovación (Agencia I+D+i, PICT-2018-03743), and Universidad Nacional de La Plata (G11-150), Argentina., With funding from the Spanish government through the Severo Ochoa Centre of Excellence accreditation SEV-2017-0709.

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. 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., Comment: 18 pages, 11 figures, 3tables; accepted for publication in MNRAS

While major mergers have long been proposed as a driver of both AGN activity and the M-sigma relation, studies of moderate to high redshift Seyfert-luminosity AGN hosts have found little evidence for enhanced rates of interactions. However, both theory and observation suggest that while these AGN may be fueled by stochastic accretion and secular processes, high-luminosity, high-redshift, and heavily obscured AGN are the AGN most likely to be merger-driven. To better sample this population of AGN, we turn to infrared selection in the CANDELS/COSMOS field. Compared to their lower-luminosity and less obscured X-ray-only counterparts, IR-only AGN (luminous, heavily obscured AGN) are more likely to be classified as either irregular (50$^{+12}_{-12}$% vs. 9$^{+5}_{-2}$%) or asymmetric (69$^{+9}_{-13}$% vs. 17$^{+6}_{-4}$%) and are less likely to have a spheroidal component (31$^{+13}_{-9}$% vs. 77$^{+4}_{-6}$%). Furthermore, IR-only AGN are also significantly more likely than X-ray-only AGN (75$^{+8}_{-13}$% vs. 31$^{+6}_{-6}$%) to be classified either as interacting or merging in a way that significantly disturbs the host galaxy or disturbed though not clearly interacting or merging, which potentially represents the late stages of a major merger. This suggests that while major mergers may not contribute significantly to the fueling of Seyfert luminosity AGN, interactions appear to play a more dominant role in the triggering and fueling of high-luminosity heavily obscured AGN., 13 pages, 7 figures, 1 table, Accepted for publication in the Astrophysical Journal

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., 14 pages, 8 figures, 3 tables. Submitted to MNRAS

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., 25 pages, 19 figures, 7 tables. Accepted for publication in MNRAS

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., 25 pages, 15 figures, 5 tables. Accepted for publication in MNRAS