We introduce a parametric family of models to characterize the properties of astrophysical systems in a quasi-stationary evolution under the incidence evaporation .
We start from an one-particle distribution f _ { \gamma } \left ( \mathbf { q } , \mathbf { p } | \beta, \varepsilon _ { s } \right ) that considers an appropriate deformation of Maxwell-Boltzmann form with inverse temperature \beta , in particular , a power-law truncation at the scape energy \varepsilon _ { s } with exponent \gamma > 0 .
This deformation is implemented using a generalized \gamma -exponential function obtained from the fractional integration of ordinary exponential .
As shown in this work , this proposal generalizes models of tidal stellar systems that predict particles distributions with isothermal cores and polytropic haloes , e.g .
: Michie-King models .
We perform the analysis of 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 whenever deformation parameter \gamma < \gamma _ { c } \simeq 2.13 . PACS numbers : 05.20.-y , 05.70.-a Keywords : astrophysical systems , evaporation , thermo-statistics E-mail : yuvineza.gomez @ gmail.com ; lvelazquez @ ucn.cl