Testing a Coupling Relation between Visible and Dark Matter in the MS 2137−2353 Cluster Core

Abstract

The empirical coupling relation in Md=γM1/2r between the halo dark mass distribution Md and the visible mass M at radius r, previously demonstrated for spiral galaxies, is extrapolated to the case of a simple cluster core with mass distribution constrained by a lens mass model. In the at present unique case of MS 2137-2353, where the lens model density profile may be constrained from ~10 h50-1 kpc to ~100 h50-1 kpc because of the presence of a radial arc, the density profile deduced from the coupling relation is found to be consistent with that deduced from lens modeling. The coupling relation predicts very sharp cluster cores. In the case of a cluster such as Abell 2218, where a lens model cannot be tested in the innermost region, the density distribution deduced from the structural relation is more sharply peaked than an isothermal lens model, but the density distributions in the overlap region are consistent.