Stellar polytropes and Navarro-Frenk-White halo models: comparison with   observations
  Motivated by the possible conflict between the Navarro-Frenk-White(NFW) model predictions for the dark matter contents of galactic systems and its correlation with baryonic surface density, we will explore an alternative paradigm for the description of dark matter halos. Such an alternative emerges from Tsallis' non-extensive thermodynamics applied to self-gravitating systems and leads to the so-called ``stellar polytrope'' (SP) model. We consider that this could be a better approach to real structures rather than the isothermal model, given the fact that the first one takes into account the non-extensivity of energy and entropy present in these type of systems characterized by long-range interactions. We compare a halo based on the Navarro-Frenk-White (NFW) and one which follows the SP description. Analyzing the dark matter contents estimated by means of global physical parameters of galactic disks, obtained from a sample of actual galaxies, with the ones of the unobserved dark matter halos, we conclude that the SP model is favored over the NFW model in such a comparison. 
Jesus Zavala, Dario Nunez, Roberto A. Sussman, Luis G. Cabral-Rosetti   and Tonatiuh Matos