The total mass of a galaxy cluster is one of its most fundamental properties. Together with the redshift, the mass links observation and theory, allowing us to use the cluster population to test ...models of structure formation and to constrain cosmological parameters. Building on the rich heritage from X-ray surveys, new results from Sunyaev-Zeldovich and optical surveys have stimulated a resurgence of interest in cluster cosmology. These studies have generally found fewer clusters than predicted by the baseline
Planck
Λ
CDM model, prompting a renewed effort on the part of the community to obtain a definitive measure of the true cluster mass scale. Here we review recent progress on this front. Our theoretical understanding continues to advance, with numerical simulations being the cornerstone of this effort. On the observational side, new, sophisticated techniques are being deployed in individual mass measurements and to account for selection biases in cluster surveys. We summarise the state of the art in cluster mass estimation methods and the systematic uncertainties and biases inherent in each approach, which are now well identified and understood, and explore how current uncertainties propagate into the cosmological parameter analysis. We discuss the prospects for improvements to the measurement of the mass scale using upcoming multi-wavelength data, and the future use of the cluster population as a cosmological probe.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We present an analysis of the relation between the masses of cluster- and group-sized haloes, extracted from Λ cold dark matter (ΛCDM) cosmological N-body and hydrodynamic simulations, and their ...velocity dispersion at different redshifts from z = 2 to 0. The main aim of this analysis is to understand how the implementation of baryonic physics in simulations affects such relations, i.e. to what extent the use of the velocity dispersion as a proxy for cluster mass determination is hampered by the imperfect knowledge of the baryonic physics. In our analysis, we use several sets of simulations with different physics implemented: one DM-only simulation, one simulation with non-radiative gas, and two radiative simulations, one of which with feedback from active galactic nuclei. Velocity dispersions are determined using three different tracers: DM particles, subhaloes and galaxies.
We confirm that DM particles trace a relation that is fully consistent with the theoretical expectations based on the virial theorem, σv ∝ M
α with α = 1/3, and with previous results presented in the literature. On the other hand, subhaloes and galaxies trace steeper relations, with velocity dispersion scaling with mass with α > 1/3, and with larger values of the normalization. Such relations imply that galaxies and subhaloes have a ∼10 per cent velocity bias relative to the DM particles, which can be either positive or negative, depending on the halo mass, redshift and physics implemented in the simulation.
We explain these differences as due to dynamical processes, namely dynamical friction and tidal disruption, acting on substructures and galaxies, but not on DM particles. These processes appear to be more or less effective, depending on the halo masses and the importance of baryon cooling, and may create a non-trivial dependence of the velocity bias and the σ1D-M
200 relation on the tracer, the halo mass and its redshift.
These results are relevant in view of the application of velocity dispersion as a proxy for cluster masses in ongoing and future large redshift surveys.
We report the spectroscopic confirmation of 22 new multiply lensed sources behind the Hubble Frontier Field (HFF) galaxy cluster MACS J0416.1−2403 (MACS 0416), using archival data from the Multi Unit ...Spectroscopic Explorer (MUSE) on the VLT. Combining with previous spectroscopic measurements of 15 other multiply imaged sources, we have obtained a sample of 102 secure multiple images with measured redshifts, the largest to date in a single strong lensing system. The newly confirmed sources are largely low-luminosity Lyman-α emitters with redshift in the range 3.08−6.15 . With such a large number of secure constraints, and a significantly improved sample of galaxy members in the cluster core, we have improved our previous strong lensing model and obtained a robust determination of the projected total mass distribution of MACS 0416. We find evidence of three cored dark-matter halos, adding to the known complexity of this merging system. The total mass density profile, as well as the sub-halo population, are found to be in good agreement with previous works. We update and make public the redshift catalog of MACS 0416 from our previous spectroscopic campaign with the new MUSE redshifts. We also release lensing maps (convergence, shear, magnification) in the standard HFF format.
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Aims. We aim to compute the mass and velocity anisotropy profiles of Abell 2142 and, from there, the pseudo phase–space density profile Q(r) and the density slope − velocity anisotropy β − γ ...relation, and then to compare them with theoretical expectations. Methods. The mass profiles were obtained by using three techniques based on member galaxy kinematics, namely the caustic method, the method of dispersion-kurtosis, and MAMPOSSt. Through the inversion of the Jeans equation, it was possible to compute the velocity anisotropy profiles. Results. The mass profiles, as well as the virial values of mass and radius, computed with the different techniques agree with one another and with the estimates coming from X-ray and weak lensing studies. A combined mass profile is obtained by averaging the lensing, X-ray, and kinematics determinations. The cluster mass profile is well fitted by an NFW profile with c = 4.0 ± 0.5. The population of red and blue galaxies appear to have a different velocity anisotropy configuration, since red galaxies are almost isotropic, while blue galaxies are radially anisotropic, with a weak dependence on radius. The Q(r) profile for the red galaxy population agrees with the theoretical results found in cosmological simulations, suggesting that any bias, relative to the dark matter particles, in velocity dispersion of the red component is independent of radius. The β − γ relation for red galaxies matches the theoretical relation only in the inner region. The deviations might be due to the use of galaxies as tracers of the gravitational potential, unlike the non–collisional tracer used in the theoretical relation.
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We carried out a detailed strong lensing analysis of a sub-sample of eight galaxy clusters of the Cluster Lensing And Supernova survey with Hubble (CLASH) in the redshift range of zcluster = 0.23 − ...0.59 using extensive spectroscopic information, primarily from the Multi Unit Spectroscopic Explorer (MUSE) archival data and complemented with CLASH-VLT redshift measurements. The observed positions of the multiple images of strongly lensed background sources were used to constrain parametric models describing the cluster total mass distributions. Different models were tested in each cluster depending on the complexity of its mass distribution and on the number of detected multiple images. Four clusters show more than five spectroscopically confirmed multiple image families. In this sample, we did not make use of families that are only photometrically identified in order to reduce model degeneracies between the values of the total mass of a cluster source redshifts, in addition to systematics due to the potential misidentifications of multiple images. For the remaining four clusters, we used additional families without any spectroscopic confirmation to increase the number of strong lensing constraints up to the number of free parameters in our parametric models. We present spectroscopic confirmation of 27 multiply lensed sources, with no previous spectroscopic measurements, spanning over the redshift range of zsrc = 0.7 − 6.1. Moreover, we confirm an average of 48 galaxy members in the core of each cluster thanks to the high efficiency and large field of view of MUSE. We used this information to derive precise strong lensing models, projected total mass distributions, and magnification maps. We show that, despite having different properties (i.e. number of mass components, total mass, redshift, etc.), the projected total mass and mass density profiles of all clusters have very similar shapes when rescaled by independent measurements of M200c and R200c. Specifically, we measured the mean value of the projected total mass of our cluster sample within 10 (20)% of R200c to be 0.13 (0.32) of M200c, with a remarkably small scatter of 5 (6)%. Furthermore, the large number of high-z sources and the precise magnification maps derived in this work for four clusters add up to the sample of high-quality gravitational telescopes to be used to study the faint and distant Universe.
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Context. The relation between a cosmological halo concentration and its mass (cMr) is a powerful tool to constrain cosmological models of halo formation and evolution. Aims. On the scale of galaxy ...clusters the cMr has so far been determined mostly with X-ray and gravitational lensing data. The use of independent techniques is helpful in assessing possible systematics. Here we provide one of the few determinations of the cMr by the dynamical analysis of the projected-phase-space distribution of cluster members. Methods. Based on the WINGS and OmegaWINGS data sets, we used the Jeans analysis with the MAMPOSSt technique to determine masses and concentrations for 49 nearby clusters, each of which has ≳60 spectroscopic members within the virial region, after removal of substructures. Results. Our cMr is in statistical agreement with theoretical predictions based on ΛCDM cosmological simulations. Our cMr is different from most previous observational determinations because of its flatter slope and lower normalization. It is however in agreement with two recent cMr obtained using the lensing technique on the CLASH and LoCuSS cluster data sets. Conclusions. The dynamical study of the projected-phase-space of cluster members is an independent and valid technique to determine the cMr of galaxy clusters. Our cMr shows no tension with theoretical predictions from ΛCDM cosmological simulations for low-redshift, massive galaxy clusters. In the future we will extend our analysis to galaxy systems of lower mass and at higher redshifts.
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We present an improved determination of the total mass distribution of three massive clusters from the Cluster Lensing and Supernova Survey with Hubble and Hubble Frontier Fields, MACS J1206.2−0847 ...(z = 0.44), MACS J0416.1−2403 (z = 0.40), Abell S1063 (z = 0.35). We specifically reconstructed the sub-halo mass component with robust stellar kinematics information of cluster galaxies, in combination with precise strong lensing models based on large samples of spectroscopically identified multiple images. We used integral-field spectroscopy in the cluster cores, from the Multi Unit Spectroscopic Explorer on the Very Large Telescope, to measure the stellar velocity dispersion, σ, of 40−60 member galaxies per cluster, covering four to five magnitudes to mF160W ≃ 21.5. We verified the robustness and quantified the accuracy of the velocity dispersion measurements with extensive spectral simulations. With these data, we determined the normalization and slope of the galaxy L–σ Faber–Jackson relation in each cluster and used these parameters as a prior for the scaling relations of the sub-halo population in the mass distribution modeling. When compared to our previous lens models, the inclusion of member galaxies’ kinematics provides a similar precision in reproducing the positions of the multiple images. However, the inherent degeneracy between the central effective velocity dispersion, σ0, and truncation radius, rcut, of sub-halos is strongly reduced, thus significantly alleviating possible systematics in the measurements of sub-halo masses. The three independent determinations of the σ0 − rcut scaling relation in each cluster are found to be fully consistent, enabling a statistical determination of sub-halo sizes as a function of σ0, or halo masses. Finally, we derived the galaxy central velocity dispersion functions of the three clusters projected within 16% of their virial radius, finding that they are well in agreement with each other. We argue that such a methodology, when applied to high-quality kinematics and strong lensing data, allows the sub-halo mass functions to be determined and compared with those obtained from cosmological simulations.
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We study the characteristics of the galaxy cluster samples expected from the European Space Agency's Euclid satellite and forecast constraints on parameters describing a variety of cosmological ...models. In this paper we use the same method of analysis already adopted in the Euclid
Red
Book, which is based on the Fisher matrix approach. Based on our analytical estimate of the cluster selection function in the photometric Euclid survey, we forecast the constraints on cosmological parameters corresponding to different extensions of the standard Λ cold dark matter model. Using only Euclid clusters, we find that the amplitude of the matter power spectrum will be constrained to Δσ8 = 0.0014 and the mass density parameter to ΔΩm = 0.0011. The dynamical evolution of dark energy will be constrained to Δw
0 = 0.03 and Δw
a
= 0.2 with free curvature Ω
k
, resulting in a (w
0, w
a
) figure of merit (FoM) of 291. In combination with Planck cosmic microwave background (CMB) constraints, the amplitude of primordial non-Gaussianity will be constrained to Δf
NL ≃ 6.6 for the local shape scenario. The growth factor parameter γ, which signals deviations from general relativity, will be constrained to Δγ = 0.02, and the neutrino density parameter to ΔΩν = 0.0013 (or Δ∑m
ν = 0.01). Including the Planck CMB covariance matrix improves dark energy constraints to Δw
0 = 0.02, Δw
a
= 0.07, and a FoM = 802. Knowledge of the observable–cluster mass scaling relation is crucial to reach these accuracies. Imaging and spectroscopic capabilities of Euclid will enable internal mass calibration from weak lensing and the dynamics of cluster galaxies, supported by external cluster surveys.
Abstract
We use galaxy dynamical information to calibrate the richness–mass scaling relation of a sample of 428 galaxy clusters that are members of the CODEX sample with redshifts up to z ∼ 0.7. ...These clusters were X-ray selected using the ROSAT All-Sky Survey (RASS) and then cross-matched to associated systems in the redMaPPer (the red sequence Matched-filter Probabilistic Percolation) catalogue from the Sloan Digital Sky Survey. The spectroscopic sample we analyse was obtained in the SPIDERS program and contains ∼7800 red member galaxies. Adopting NFW mass and galaxy density profiles and a broad range of orbital anisotropy profiles, we use the Jeans equation to calculate halo masses. Modelling the scaling relation as $\lambda \propto \text{A}_{\lambda } {M_{\text{200c}}}^{\text{B}_{\lambda }} ({1+z})^{\gamma _{\lambda }}$, we find the parameter constraints $\text{A}_{\lambda }=38.6^{+3.1}_{-4.1}\pm 3.9$, $\text{B}_{\lambda }=0.99^{+0.06}_{-0.07}\pm 0.04$, and $\gamma _{\lambda }=-1.13^{+0.32}_{-0.34}\pm 0.49$, where we present systematic uncertainties as a second component. We find good agreement with previously published mass trends with the exception of those from stacked weak lensing analyses. We note that although the lensing analyses failed to account for the Eddington bias, this is not enough to explain the differences. We suggest that differences in the levels of contamination between pure redMaPPer and RASS + redMaPPer samples could well contribute to these differences. The redshift trend we measure is more negative than but statistically consistent with previous results. We suggest that our measured redshift trend reflects a change in the cluster galaxy red sequence (RS) fraction with redshift, noting that the trend we measure is consistent with but somewhat stronger than an independently measured redshift trend in the RS fraction. We also examine the impact of a plausible model of correlated scatter in X-ray luminosity and optical richness, showing it has negligible impact on our results.
When clusters of galaxies are viewed in projection, one cannot avoid picking up a fraction of foreground/background interlopers, that lie within the virial cone, but outside the virial sphere. ...Structural and kinematic deprojection equations are known for the academic case of a static Universe, but not for the real case of an expanding Universe, where the Hubble flow (HF) stretches the line-of-sight distribution of velocities. Using 93 mock relaxed clusters, built from the dark matter (DM) particles of a hydrodynamical cosmological simulation, we quantify the distribution of interlopers in projected phase space (PPS), as well as the biases in the radial and kinematical structure of clusters produced by the HF. The stacked mock clusters are well fit by an m = 5 Einasto DM density profile (but only out to 1.5 virial radii), with velocity anisotropy (VA) close to the Mamon-Łokas model with characteristic radius equal to that of density slope -2. The surface density of interlopers is nearly flat out to the virial radius, while their velocity distribution shows a dominant Gaussian cluster-outskirts component and a flat field component. This distribution of interlopers in PPS is nearly universal, showing only small trends with cluster mass, and is quantified. A local κ = 2.7 sigma velocity cut is found to return the line-of-sight velocity dispersion profile (LOSVDP) expected from the NFW density and VA profiles measured in three dimensions. The HF causes a shallower outer LOSVDP that cannot be well matched by the Einasto model for any value of κ. After this velocity cut, which removes 1 interloper out of 6, interlopers still account for 23 ± 1% of all DM particles with projected radii within the virial radius (surprisingly very similar to the observed fraction of cluster galaxies lying off the Red Sequence) and over 60% between 0.8 and 1 virial radius. The HF causes the best-fit projected NFW or m = 5 Einasto model to the stacked cluster to underestimate the true concentration measured in 3D by 6 ± 6% (16 7%) after (before) the velocity cut. These biases in concentration are reduced by over a factor two once a constant background is included in the fit. The VA profile recovered from the measured LOSVDP by assuming the correct mass profile recovers fairly well the VA measured in 3D, with a slight, marginally significant, bias towards more radial orbits in the outer regions. These small biases in the concentration and VA of the galaxy system are overshadowed by important cluster-to-cluster fluctuations caused by cosmic variance and by the strong inefficiency caused by the limited numbers of observed galaxies in clusters. An appendix provides an analytical approximation to the surface density, projected mass and tangential shear profiles of the Einasto model. Another derives the expressions for the surface density and mass profiles of the NFW model projected on the sphere (for future kinematic modeling). Appendices are only available in electronic form at www.aanda.org
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