Flat-cored Dark Matter in Cuspy Clusters of Galaxies

Sand, Treu Ellis (2002) have measured the central density profile of cluster MS2137-23 with gravitational lensing and velocity dispersion and removed the stellar contribution with a reasonable M/L. The resulting dark matter (DM) distribution within r 50h −1 kpc was fitted by a density cusp of r −β with β = 0.35, in an apparent contradiction to the CDM prediction of β ∼ 1. The disagreement worsens if adiabatic compression of the DM by the infalling baryons is considered. Following El-Zant, Shlosman Hoffman (2001), we argue that dynamical friction acting on galaxies moving within the DM background counters the effect of adiabatic compression by transfering their orbital energy to the DM, thus heating up and softening the cusp. Using N-body simulations we show that indeed the inner DM distribution flattens (with β ≈ 0.35 for a cluster like MS2137-23) when the galaxies spiral inward. We find as a robust result that while the DM distribution becomes core-like, the overall mass distribution preserves its cuspy nature, in agreement with X-ray and lensing observations of clusters.