# Concerning pressure and entropy of shock-accelerated heliosheath electrons

## TL;DR

This paper models the behavior of shock-accelerated electrons in the heliosheath, deriving pressure and entropy evolution equations, and concludes that the electron fluid behaves as an isobaric and isentropic flow downstream of the termination shock.

## Contribution

It introduces a kinetic transport framework with a local kappa distribution to analyze electron pressure and entropy evolution in the heliosheath, revealing flow characteristics.

## Key findings

- Electron pressure can be expressed as a function of streamline coordinate.
- The electron fluid in the heliosheath is essentially isobaric and isentropic.
- The derived equations describe the evolution of electron pressure and entropy downstream of the shock.

## Abstract

We study the behaviour of shocked wind-electrons leaving wind-driving stars after undergoing the outer wind termination shock. As an example, we describe the evolution of the keV-energetic electron distribution function downstream of the heliospheric termination shock. We start from a kinetic transport equation in the bulk frame of the heliosheath plasma flow taking into account shock-induced electron injection, convective changes, cooling processes, and whistler wave-induced energy diffusion. From this equation we proceed to an associated pressure moment of the electron distribution function arriving at a corresponding pressure transport equation which describes the evolution of the electron pressure in the bulk frame of the plasma along the plasma flow lines. We assume that the local distribution function, in view of the prevailing non-LTE conditions, is represented by a local kappa function with local kappa parameters that vary with the streamline coordinate $s$ downstream of the solar wind termination shock. We obtain the solution for the electron pressure as a function of the streamline coordinate $s$ from the pressure transport equation and demonstrate that, connected with this pressure, one obtains an expression for the entropy of the electron fluid which can also be derived as a streamline function. We show that the heliosheath electron fluid can essentially be characterized as an isobaric and isentropic flow. These results allow to generally conclude that astrotail plasma flows are characterized as such flows.