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Cluster mass profiles are tests of models of structure formation. Only two current observational methods of determining the mass profile, gravitational lensing and the caustic technique, are independent of the assumption of dynamical equilibrium. Both techniques enable determination of the extended mass profile at radii beyond the virial radius. For 19 clusters, we compare the mass profile based on the caustic technique with weak lensing measurements taken from the literature. This comparison offers a test of systematic issues in both techniques. Around the virial radius, the two methods of mass estimation agree to within about 30%, consistent with the expected errors in the individual techniques. At small radii, the caustic technique overestimates the mass as expected from numerical simulations. The ratio between the lensing profile and the caustic mass profile at these radii suggests that the weak lensing profiles are a good representation of the true mass profile. At radii larger than the virial radius, the lensing mass profile exceeds the caustic mass profile possibly as a result of contamination of the lensing profile by large-scale structures within the lensing kernel. We highlight the case of the closely neighboring clusters MS0906+11 and A750 to illustrate the potential seriousness of contamination of the the weak lensing signal by unrelated structures.
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We use 1 kpc resolution cosmological AMR simulations of a Virgo-like galaxy cluster to investigate the effect of feedback from supermassive black holes (SMBH) on the mass distribution of dark matter, gas and stars. We compared three different models: (i) a standard galaxy formation model featuring gas cooling, star formation and supernovae feedback, (ii) a quenching model for which star formation is artificially suppressed in massive halos and finally (iii) the recently proposed AGN feedback model of Booth & Schaye (2009). Without AGN feedback (even in the quenching case), our simulated cluster suffers from a strong overcooling problem, with a stellar mass fraction significantly above observed values in M87. The baryon distribution is highly concentrated, resulting in a strong adiabatic contraction (AC) of dark matter. With AGN feedback, on the contrary, the stellar mass in the bright central galaxy (BCG) lies below observational estimates and the overcooling problem disappears. The stellar mass of the BCG is seen to increase with increasing mass resolution, suggesting that our stellar masses converges to the correct value from below. The gas and total mass distributions are in striking agreement with observations. We also find a slight deficit (~10%) of baryons at the virial radius, due to the effect of AGN-driven shock waves pushing gas to Mpc scales and beyond. This baryon deficit results in a slight adiabatic expansion of the dark matter distribution, that can be explained quantitatively by AC theory.
We present measurements of the radial profiles of the mass and galaxy number density around Sunyaev-Zeldovich-selected clusters using both weak lensing and galaxy counts. The clusters are selected from the Atacama Cosmology Telescope Data Release 5 and the galaxies from the Dark Energy Survey Year 3 dataset. With signal-to-noise of 62 (43) for galaxy (weak lensing) profiles over scales of about $0.2-20h^{-1}$ Mpc, these are the highest precision measurements for SZ-selected clusters to date. Because SZ selection closely approximates mass selection, these measurements enable several tests of theoretical models of the mass and light distribution around clusters. Our main findings are: 1. The splashback feature is detected at a consistent location in both the mass and galaxy profiles and its location is consistent with predictions of cold dark matter N-body simulations. 2. The full mass profile is also consistent with the simulations; hence it can constrain alternative dark matter models that modify the mass distribution of clusters. 3. The shapes of the galaxy and lensing profiles are remarkably similar for our sample over the entire range of scales, from well inside the cluster halo to the quasilinear regime. This can be used to constrain processes such as quenching and tidal disruption that alter the galaxy distribution inside the halo, and scale-dependent features in the transition regime outside the halo. We measure the dependence of the profile shapes on the galaxy sample, redshift and cluster mass. We extend the Diemer & Kravtsov model for the cluster profiles to the linear regime using perturbation theory and show that it provides a good match to the measured profiles. We also compare the measured profiles to predictions of the standard halo model and simulations that include hydrodynamics. Applications of these results to cluster mass estimation and cosmology are discussed.
In this work we study the shape of the projected surface mass density distribution of galaxy clusters using weak-lensing stacking techniques. In particular, we constrain the average aligned component of the projected ellipticity, $epsilon$, for a sample of redMaPPer clusters ($0.1 leq z < 0.4$). We consider six different proxies for the cluster orientation and measure $epsilon$ for three ranges of projected distances from the cluster centres. The mass distribution in the inner region (up to $700,$kpc) is better traced by the cluster galaxies with a higher membership probability, while the outer region (from $700,$kpc up to $5,$Mpc) is better traced by the inclusion of less probable galaxy cluster members. The fitted ellipticity in the inner region is $epsilon = 0.21 pm 0.04$, in agreement with previous estimates. We also study the relation between $epsilon$ and the cluster mean redshift and richness. By splitting the sample in two redshift ranges according to the median redshift, we obtain larger $epsilon$ values for clusters at higher redshifts, consistent with the expectation from simulations. In addition, we obtain higher ellipticity values in the outer region of clusters at low redshifts. We discuss several systematic effects that might affect the measured lensing ellipticities and their relation to the derived ellipticity of the mass distribution.
The cosmological parameters prefered by the cosmic microwave background (CMB) primary anisotropies predict many more galaxy clusters than those that have been detected via the thermal Sunyaev-Zeldovich (tSZ) effect. This tension has attracted considerable attention since it could be evidence of physics beyond the simplest $Lambda$CDM model. However, an accurate and robust calibration of the mass-observable relation for clusters is necessary for the comparison, which has been proven difficult to obtain so far. Here, we present new contraints on the mass-pressure relation by combining tSZ and CMB lensing measurements about optically-selected clusters. Consequently, our galaxy cluster sample is independent from the data employed to derive cosmological constrains. We estimate an average hydrostatic mass bias of $b = 0.26 pm 0.07$, with no significant mass nor redshift evolution. This value greatly reduces the tension between the predictions of $Lambda$CDM and the observed abundance of tSZ clusters while being in agreement with recent estimations from tSZ clustering. On the other hand, our value for $b$ is higher than the predictions from hydro-dynamical simulations. This suggests the existence of mechanisms driving large departures from hydrostatic equilibrium and that are not included in state-of-the-art simulations, and/or unaccounted systematic errors such as biases in the cluster catalogue due to the optical selection.
We present the analysis of a local (z = 0.04 - 0.2) sample of 31 galaxy clusters with the aim of measuring the density of the X-ray emitting gas in cluster outskirts. We compare our results with numerical simulations to set constraints on the azimuthal symmetry and gas clumping in the outer regions of galaxy clusters. We exploit the large field-of-view and low instrumental background of ROSAT/PSPC to trace the density of the intracluster gas out to the virial radius. We perform a stacking of the density profiles to detect a signal beyond r200 and measure the typical density and scatter in cluster outskirts. We also compute the azimuthal scatter of the profiles with respect to the mean value to look for deviations from spherical symmetry. Finally, we compare our average density and scatter profiles with the results of numerical simulations. As opposed to some recent Suzaku results, and confirming previous evidence from ROSAT and Chandra, we observe a steepening of the density profiles beyond sim r500. Comparing our density profiles with simulations, we find that non-radiative runs predict too steep density profiles, whereas runs including additional physics and/or treating gas clumping are in better agreement with the observed gas distribution. We report for the first time the high-confidence detection of a systematic difference between cool-core and non-cool core clusters beyond sim 0.3r200, which we explain by a different distribution of the gas in the two classes. Beyond sim r500, galaxy clusters deviate significantly from spherical symmetry, with only little differences between relaxed and disturbed systems. We find good agreement between the observed and predicted scatter profiles, but only when the 1% densest clumps are filtered out in the simulations. [Abridged]
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