Abstract

We introduce a parametric family of models in order to characterize the properties of astrophysical systems in quasi-stationary evolution under the influence of evaporation. We start from a one-particle distribution p d, that is based on an appropriate deformation of Maxwell-Boltzmann form with inverse temperature 3 and, in particular, a power-law It at the escape energy with exponent gamma > 0. This deformation is implemented using a generalized gamma-exponential function obtained from the fractional integration of an ordinary exponential. As shown in this work. this proposal generalizes models of tidal stellar systems that predict particle distributions with isothermal cores ana polytropic haloes, e.g. Michie-King models. We perform an analysis of the thermodynamic features of these models and their associated distribution profiles. A nontrivial consequence of this study is that profiles with isothermal cores and polytropic haloes are only obtained for low energies the deformation gamma < gamma(c) similar or equal to 2.13.