On the interpretation and applicability of $\kappa$-distributions

TL;DR

This paper clarifies the correct interpretation of $5$-distributions in space plasma physics, emphasizing the importance of choosing the appropriate model based on the physical system to avoid unphysical results.

Contribution

It provides a quantitative comparison of two interpretations of $5$-distributions, guiding correct application based on system characteristics.

Findings

Both distribution alternatives are valid but apply to different physical systems.

Incorrect choice of interpretation can lead to unphysical results.

Guidelines for selecting the appropriate $5$-distribution based on system nature.

Abstract

The generally accepted representation of $\kappa$-distributions in space plasma physics allows for two different alternatives, namely assuming either the temperature or the thermal velocity to be $\kappa$-independent. The present paper aims to clarify the issue concerning which of the two possible choices and the related physical interpretation is the correct one. A quantitative comparison of the consequences of the use of both distributions for specific physical systems leads to their correct interpretation. It is found that both alternatives can be realized, but are valid for principally different physical systems. The investigation demonstrates that, before employing one of the two alternatives, one should be conscious about the nature of the physical system one intends to describe, otherwise one would possibly obtain unphysical results.