On the Density profile slope of Clusters of Galaxies
  The present paper extends to clusters of galaxies the study of Del Popolo (2012), concerning how the baryon-dark matter (DM) interplay shapes the density profile of dwarf galaxies. Cluster density profiles are determined taking into account dynamical friction, random and ordered angular momentum and the response of dark matter halos to condensation of baryons. We find that halos containing only DM are characterized by Einasto's profiles, and that the profile flattens with increasing content of baryons, and increasing values of random angular momentum. The analytical results obtained in the first part of the paper were applied to well studied clusters whose inner profiles have slopes flatter than NFW predictions (A611, A383) or are characterized by profiles in agreement with the NFW model (MACS J1423.8+2404, RXJ1133). By using independently-measured baryonic fraction, a typical spin parameter value $\lambda \simeq 0.03$, and adjusting the random angular momentum, we re-obtain the mass and density profiles of the quoted clusters. Finally, we show that the baryonic mass inside $\simeq 10$ kpc, $M_{b,in}$ is correlated with the total mass of the clusters, %finding a correlation among the two quantities, as $M_{b,in} \propto M_{500}^{0.4}$. 
A. Del Popolo ((1) Department of Physics and Astronomy, Catania   University, Italy (2) Departamento de Astronomia, Universi...
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