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 .