CLASH-VLT: The Inner Slope of the MACS J1206.2-0847 Dark Matter Density Profile

The inner slope (gamma DM) of the dark matter (DM) density profile of cosmological halos carries information about the properties of DM and/or baryonic processes affecting the halo gravitational potential. Cold DM cosmological simulations predict steep inner slopes, gamma DM similar or equal to 1. We test this prediction on the MACS J1206.2-0847 cluster at redshift z = 0.44, whose DM density profile has been claimed to be cored at the center. We determine the cluster DM density profile from 2 kpc from the cluster center to the virial radius (similar to 2 Mpc), using the velocity distribution of similar or equal to 500 cluster galaxies and the internal velocity dispersion profile of the Brightest Cluster Galaxy (BCG), obtained from VIMOS@VLT and MUSE@VLT data. We solve the Jeans equation of dynamical equilibrium using an upgraded version of the MAMPOSSt method. The total mass profile is modeled as a sum of a generalized Navarro-Frenk-White profile that describes the DM component, allowing for a free inner slope of the density profile, a Jaffe profile that describes the BCG stellar mass component, and a nonparametric baryonic profile that describes the sum of the remaining galaxy stellar mass and of the hot intra-cluster gas mass. Our total mass profile is in remarkable agreement with independent determinations based on X-ray observations and strong lensing. We find gamma DM=0.7-0.1+0.2 (68% confidence levels), consistent with predictions from recent Lambda cold dark matter cosmological numerical simulations.