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Register a new userThe galaxy cluster mass scale and its impact on cosmological constraints from the cluster population
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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 LCDM 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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In recent years, the availability of large, complete cluster samples has enabled numerous cosmological parameter inference analyses using cluster number counts. These have provided constraints on the cosmic matter density $Omega_m$ and the amplitude of matter density fluctuations $sigma_8$ alternative to those obtained from other standard probes. However, systematics uncertainties, such as the mass calibration bias and selection effects, may still significantly affect these data analyses. Hence, it is timely to explore other proxies of galaxy cluster cosmology that can provide cosmological constraints complementary to those obtained from cluster number counts. Here, we use measurements of the cluster sparsity from weak lensing mass estimates of the LC$^2$-{it single} and HSC-XXL cluster catalogs to infer constraints on a flat $Lambda$CDM model. The cluster sparsity has the advantage of being insensitive to selection and mass calibration bias. On the other hand, it primarily constrains a degenerate combination of $Omega_m$ and $sigma_8$ (along approximately constant curves of $S_8=sigma_8sqrt{Omega_m/0.3}$), and to less extent the reduced Hubble parameter $h$. Hence, in order to break the internal parameter degeneracies we perform a combined likelihood analysis of cluster sparsities with cluster gas mass fraction measurements and BAO data. We find marginal constraints that are competitive with those from other standard cosmic probes: $Omega_m=0.316pm 0.013$, $sigma_8=0.757pm 0.067$ (corresponding to $S_8=0.776pm 0.064$) and $h=0.696pm 0.017$ at $1sigma$. Moreover, assuming a conservative Gaussian prior on the mass bias of gas mass fraction data, we find a lower limit on the gas depletion factor $Y_{b,500c}gtrsim 0.89$.
Galaxy cluster number count has been proven to be a powerful cosmological probe. However, cosmological constraints established with galaxy cluster number count are highly dependent on the calibration of the mass-observable relations. Thanks to its nearly mass independence the specific mass accretion rate of galaxy clusters is nearly insensitive to the calibration of mass-observable relations. The study of galaxy cluster number count evolution allows to probe the galaxy cluster mass accretion history in the context of an homogenous Universe. In this paper, we use relative abundance matching to infer the galaxy cluster mass accretion rate (MAR) for $z in [0.0,0.6[$. Then, we use the MAR to set cosmological constraints. We found that this cosmological probe is sensitive to $sigma_8 Omega_{rm m}^{-0.3} H_0^{-0.2}$ whereas the galaxy cluster count is sensitive to $sigma_8 Omega_{rm m}^{0.3}$. We used the second $Planck$ catalog of Sunyaev-Zeldovich sources and we derive $sigma_8 Omega_{rm m}^{-0.3} H_0^{-0.2} = 0.75 pm 0.06$. This results is consistent with cosmological constraints derived from galaxy clusters number counts, angular power spectrum, and cosmic microwave background analyses. Therefore, the MAR is a key cosmological probe that can break the $sigma_8$-$Omega_{rm m}$ degeneracy and that is not sensitive to the calibration of the mass-observable relations and does not requires a parametric form for the galaxy cluster mass-function.
Recent results by the Planck collaboration have shown that cosmological parameters derived from the cosmic microwave background anisotropies and cluster number counts are in tension, with the latter preferring lower values of the matter density parameter, $Omega_mathrm{m}$, and power spectrum amplitude, $sigma_8$. Motivated by this, we investigate the extent to which the tension may be ameliorated once the effect of baryonic depletion on the cluster mass function is taken into account. We use the large-volume Millennium Gas simulations in our study, including one where the gas is pre-heated at high redshift and one where the gas is heated by stars and active galactic nuclei (in the latter, the self-gravity of the baryons and radiative cooling are omitted). In both cases, the cluster baryon fractions are in reasonably good agreement with the data at low redshift, showing significant depletion of baryons with respect to the cosmic mean. As a result, it is found that the cluster abundance in these simulations is around 15 per cent lower than the commonly-adopted fit to dark matter simulations by Tinker et al (2008) for the mass range $10^{14}-10^{14.5}h^{-1} mathrm{M}_odot$. Ignoring this effect produces a significant artificial shift in cosmological parameters which can be expressed as $Delta[sigma_8(Omega_mathrm{m}/0.27)^{0.38}]simeq -0.03$ at $z=0.17$ (the median redshift of the $mathit{Planck}$ cluster sample) for the feedback model. While this shift is not sufficient to fully explain the $mathit{Planck}$ discrepancy, it is clear that such an effect cannot be ignored in future precision measurements of cosmological parameters with clusters. Finally, we outline a simple, model-independent procedure that attempts to correct for the effect of baryonic depletion and show that it works if the baryon-dark matter back-reaction is negligible.
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.
In some galaxy clusters powerful AGN have blown bubbles with cluster scale extent into the ambient medium. The main pressure support of these bubbles is not known to date, but cosmic rays are a viable possibility. For such a scenario copious gamma-ray emission is expected as a tracer of cosmic rays from these systems. Hydra A, the closest galaxy cluster hosting a cluster scale AGN outburst, located at a redshift of 0.0538, is investigated for being a gamma-ray emitter with the High Energy Stereoscopic System (H.E.S.S.) array and the Fermi Large Area Telescope (Fermi-LAT). Data obtained in 20.2 hours of dedicated H.E.S.S. observations and 38 months of Fermi-LAT data, gathered by its usual all-sky scanning mode, have been analyzed to search for a gamma-ray signal. No signal has been found in either data set. Upper limits on the gamma-ray flux are derived and are compared to models. These are the first limits on gamma-ray emission ever presented for galaxy clusters hosting cluster scale AGN outbursts. The non-detection of Hydra A in gamma-rays has important implications on the particle populations and physical conditions inside the bubbles in this system. For the case of bubbles mainly supported by hadronic cosmic rays, the most favorable scenario, that involves full mixing between cosmic rays and embedding medium, can be excluded. However, hadronic cosmic rays still remain a viable pressure support agent to sustain the bubbles against the thermal pressure of the ambient medium. The largest population of highly-energetic electrons which are relevant for inverse-Compton gamma-ray production is found in the youngest inner lobes of Hydra A. The limit on the inverse-Compton gamma-ray flux excludes a magnetic field below half of the equipartition value of 16 muG in the inner lobes.
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