Flat-cored dark matter in cuspy clusters of galaxies

Sand and coworkers have measured the central density profile of cluster MS 2137-23 with gravitational lensing and velocity dispersion and removed the stellar contribution with a reasonable M/L. The resulting dark matter (DM) distribution within r < 50 h(-1) kpc was fitted by a density cusp of r(-beta) with beta = 0.35, in an apparent contradiction to the cold dark matter prediction of beta similar to 1. The disagreement worsens if adiabatic compression of the DM by the infalling baryons is considered. Following El-Zant, Shlosman, & Hoffman, 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 beta approximate to 0.35 for a cluster like MS 2137-23) 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.