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Dark Matter Profiles in Clusters of Galaxies: a Phenomenological Approach

There are some basic differences between the observed properties of galaxies and clusters and the predictions from current hydrodynamical simulations. These are particularly pronounced in the central regions of galaxies and clusters. The popular NFW (Navarro, Frenk, and White) profile, for example, predicts a density cusp at the center, a behavior that (unsurprisingly) has not been observed. While it is not fully clear what are the reasons for this discrepancy, it perhaps reflects (at least partly) insufficient spatial resolution of the simulations. In this paper we explore a purely phenomenological approach to determine dark matter density profiles that are more consistent with observational results. Specifically, we deduce the gas density distribution from measured X-ray brightness profiles, and substitute it in the hydrostatic equilibrium equation in order to derive the form of dark matter profiles. Given some basic theoretical requirements from a dark matter profile, we then consider a number of simple profiles that have the desired asymptotic form. We conclude that a dark matter density profile of the form 1/(1+r/r_a)^3 is most consistent with current observational results.