Truncated $\gamma$-exponential models for tidal stellar systems

Abstract

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 $f_{\gamma }\left(\mathbf{q},\mathbf{p}|\beta ,{\epsilon }_s\right)$ that considers an appropriate deformation of Maxwell-Boltzmann form with inverse temperature $\beta$, in particular, a power-law truncation at the scape energy ${\epsilon }_s$ with exponent $\gamma >0$. This deformation is implemented using a generalized $\gamma$-exponential function obtained from the \emph{fractional integration} of ordinary exponential. As shown in this work, this proposal generalizes models of tidal stellar systems that predict particles distributions with \emph{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 $\gamma <{\gamma }_c\simeq 2.13$.

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• Self-consistent dynamical models with a finite extent -- III. Truncated power-law spheres
• Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense clusters (iii) application of pre-collapse solution to Galactic globular clusters