Stellar polytropes and Navarro--Frenk--White dark matter halos: a connection to Tsallis entropy

We present an alternative for the description of galactic halos based on Tsallis’ non–extensive entropy formalism; on this scheme, halos are stellar polytropes characterized by three parameters, the central density, ${\rho }_c$, the central velocity dispersion, ${\sigma }_c$ and the polytropic index, $n$. To evaluate these parameters we take the Navarro-Frenk-White paradigm as a comparative model and make the following assumptions: both halo models must have the same virial mass, the same total energy and the same maximal velocity. These three conditions fix all the parameters for a given stellar polytrope allowing us to compare both halo models. The halos studied have virial masses on the range ${10}^{12}-{10}^{15}{M}_{\odot }$, and it was found after the analysis that they are described, at all scales, by almost the same polytropic index, $n\approx 4.8$, implying an empirical estimation of Tsallis non–extensive parameter for this type of dynamical systems: $q\approx 1.3$.