Misestimation of temperature when applying Maxwellian distributions to space plasmas described by kappa distributions

TL;DR

This study demonstrates that assuming a Maxwellian distribution for kappa-distributed space plasmas leads to significant temperature misestimations, especially depending on the kappa index and instrument characteristics.

Contribution

It quantifies the temperature errors caused by misfitting kappa-distributed plasmas with Maxwellian models and explores the impact of instrument response on these errors.

Findings

Temperature estimates can be significantly off when using Maxwellian fits for kappa-distributed plasmas.

The error magnitude depends strongly on the kappa index and instrument response.

Fitting a Maxwellian to kappa-distributed data can lead to systematic misestimations of plasma temperature.

Abstract

This paper presents the misestimation of temperature when observations from a kappa distributed plasma are analyzed as a Maxwellian. One common method to calculate the space plasma parameters is by fitting the observed distributions using known analytical forms. More often, the distribution function is included in a forward model of the instrument's response, which is used to reproduce the observed energy spectrograms for a given set of plasma parameters. In both cases, the modeled plasma distribution fits the measurements to estimate the plasma parameters. The distribution function is often considered to be Maxwellian even though in many cases the plasma is better described by a kappa distribution. In this work we show that if the plasma is described by a kappa distribution, the derived temperature assuming Maxwell distribution can be significantly off. More specifically, we derive the plasma temperature by fitting a Maxwell distribution to pseudo-data produced by a kappa distribution, and then examine the difference of the derived temperature as a function of the kappa index. We further consider the concept of using a forward model of a typical plasma instrument to fit its observations. We find that the relative error of the derived temperature is highly depended on the kappa index and occasionally on the instrument's field of view and response.