Unified Description of Kappa-type velocity distributions

TL;DR

This paper extends Maxwell's approach to derive a broad class of Kappa velocity distributions, identifying a physically consistent fat-tailed form that fits suprathermal data without requiring an effective temperature.

Contribution

It introduces a unified framework for Kappa distributions, deriving a physically consistent fat-tailed form with a natural kinetic temperature, improving data fitting accuracy.

Findings

Identifies a physically consistent fat-tailed Kappa distribution fitting suprathermal data.

Derives a natural kinetic temperature from the model, removing the need for effective temperature.

Determines a specific value of ll that best fits the data using the physical temperature.

Abstract

An extension of Maxwell's original prescription for an ideal gas is adopted to derive a broad class of Kappa-type velocity distributions, encompassing both fat and short-tailed forms. Within this general framework, a physically consistent fat-tailed Kappa distribution is identified that accurately fits recent suprathermal data. In particular, a kinetic physical temperature $T$ emerges naturally from the model, eliminating the need to invoke an effective temperature $T_{\kappa\ell}$, as is commonly done in the literature. Finally, it is argued that only a particular value of $\ell$ ensures a satisfactory fit to the data when the physical kinetic temperature is employed.