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  1. The mass profiles of massive dark matter halos are highly sensitive to the nature of dark matter and potential modifications of the theory of gravity on large scales. The Λ cold dark matter (CDM) paradigm makes strong predictions on the shape of dark matter halos and on the dependence of the shape parameters on halo mass, such that any deviation from the predicted universal shape would have important implications for the fundamental properties of dark matter. Here we use a set of 12 galaxy clusters with available deep X-ray and Sunyaev–Zel’dovich data to constrain the shape of the gravitational field with an unprecedented level of precision over two decades in radius. We introduce a nonparametric framework to reconstruct the shape of the gravitational field under the assumption of hydrostatic equilibrium and compare the resulting mass profiles to the expectations of Navarro–Frenk–White (NFW) and Einasto parametric mass profiles. On average, we find that the NFW profile provides an excellent description of the recovered mass profiles, with deviations of less than 10% over a wide radial range. However, there appears to be more diversity in the shape of individual profiles than can be captured by the NFW model. The average NFW concentration and its scatter agree very well with the prediction of the ΛCDM framework. For a subset of systems, we disentangle the gravitational field into the contribution of baryonic components (gas, brightest cluster galaxy, and satellite galaxies) and that of dark matter. The stellar content dominates the gravitational field inside ∼0.02 R 500 but is responsible for only 1–2% of the total gravitational field inside R 200 . The total baryon fraction reaches the cosmic value at R 200 and slightly exceeds it beyond this point, possibly indicating a mild level of nonthermal pressure support (10 − 20%) in cluster outskirts. Finally, the relation between observed and baryonic acceleration exhibits a complex shape that strongly departs from the radial acceleration relation in spiral galaxies, which shows that the aforementioned relation does not hold at the galaxy-cluster scale. 
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  2. We report on the possibility of studying the proprieties of cosmic diffuse baryons by studying self-gravitating clumps and filaments connected to galaxy clusters. While filaments are challenging to detect with X-ray observations, the higher density of clumps makes them visible and a viable tracer to study the thermodynamical proprieties of baryons undergoing accretion along cosmic web filaments onto galaxy clusters. We developed new algorithms to identify these structures and applied them to a set of non-radiative cosmological simulations of galaxy clusters at high resolution. We find that in those simulated clusters, the density and temperature of clumps are independent of the mass of the cluster where they reside. We detected a positive correlation between the filament temperature and the host cluster mass. The density and temperature of clumps and filaments also tended to correlate. Both the temperature and density decrease moving outward. We observed that clumps are hotter, more massive, and more luminous if identified closer to the cluster center. Especially in the outermost cluster regions (∼3⋅ R 500,  c or beyond), X-ray observations might already have the potential to locate cosmic filaments based on the distribution of clumps and to allow one to study the thermodynamics of diffuse baryons before they are processed by the intracluster medium. 
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