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

TL;DR

This paper introduces a new family of models for tidal stellar systems using a gamma-exponential deformation of Maxwell-Boltzmann distributions, capturing systems with isothermal cores and polytropic haloes, and analyzes their thermodynamic properties.

Contribution

It presents a novel parametric family of models based on fractional exponential functions, generalizing existing tidal stellar system models with new thermodynamic insights.

Findings

Profiles with isothermal cores and polytropic haloes occur only at low energies for gamma<2.13.

The models extend Michie-King models through gamma-exponential deformation.

Thermodynamic analysis reveals conditions for different profile structures.

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 $f_{\gamma}\left(\mathbf{q},\mathbf{p}|\beta,\varepsilon_{s}\right)$ 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 \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 $\gamma<\gamma_{c}\simeq 2.13$.