The relative concentration of visible and dark matter in clusters of galaxies

In general, the best evidence for the presence of dark matter is obtained when an additional mass component with distribution different from that of the visible matter is needed to explain the dynamical data. Here we wish to study the relative distribution of visible and dark matter in clusters of galaxies, in comparison with the distribution observed on the galactic scale; in particular, we wish to check whether dark matter is more concentrated than visible matter without using assumptions or other constraints deriving from cosmology. We also intend to check whether the result depends significantly on the dynamical state of the cluster under investigation. We consider two clusters (A496 and Coma) that are representative of the two classes of cool-core and non-cool-core clusters. We first refer to a two-component dynamical model that ignores the contribution from the galaxy density distribution and study the condition of hydrostatic equilibrium for the hot intracluster medium (ICM) under the assumption of spherical symmetry, in the presence of dark matter. We model the ICM density distribution in terms of a standard beta-model with beta = 2/3, i.e. with a distribution similar to that of a regular isothermal sphere (RIS), and fit the observed X ray brightness profiles. With the explicit purpose of ignoring cosmological arguments, we naively assume that dark matter, if present, has an analogous density distribution, with the freedom of two different density and length scales. The relative distribution of visible and dark matter is then derived by fitting the temperature data for the ICM under conditions of hydrostatic equilibrium. For both clusters, we find that dark matter is more concentrated with respect to visible matter. We then test whether the conclusion changes significantly when dark matter is taken to be distributed according to cosmologically favored density profiles and when the contribution of the mass contained in galaxies is taken into account.Although the qualitative conclusions remain unchanged, we find that the contribution of galaxies to the mass budget is more important than generally assumed. We also show that, without resorting to additional information on the small scale, it is not possible to tell whether a density cusp is present or absent in these systems. In contrast with the case of individual galaxies, on the large scale in clusters of galaxies dark matter is indeed more concentrated than visible matter.