Concerning pressure and entropy of shock-accelerated heliosheath electrons

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.

Probing the thermodynamic conditions of the heliosheath plasma by shock wave propagation

“…The question then only remains as to whether or not the complete removal of contributions by particles with v ≥ c is recommended here, or whether or not a better, more physically justified calculation is needed with some compensation for the lost population. These questions have been addressed in more detail in the most recent paper by Fahr & Dutta-Roy (2019), showing that electron pressures relative to proton pressures are more reduced by this circumstance.…”

“…Here we follow calculations carried out recently by Fahr & Dutta-Roy (2019). For the initial pressures of the two fluids, i.e., electrons and protons, immediately downstream of the termination shock, assuming kappa functions f κ e (s 0 , v) and f κ i (s 0 , v) as initial distribution functions at the initial streamline coordinate s = s 0 , for example at the shock-crossing-point of Voyager-1 (see Fahr et al 2017), we find the following expressions for the ion and electron kappa pressure:…”

“…where the Θ i0 , κ i0 , and Θ e0 , κ e,0 are parameters of the initial kappa functions f κ e (s 0 , v) and f κ i (s 0 , v). With the reasonable assumption that due to charge neutrality requirements, the densities of electrons and ions downstream from the shock, after passage through the space charge layer and after flow relaxation, need to be identical, i.e., n i0 = n e0 , and with kappa parameters calculated in Fahr & Dutta-Roy (2019) this would give the following pressure ratio:…”

“…Therefore, looking back into the recent study on electron pressures in the heliosheath by Fahr & Dutta-Roy (2019) one can identify the need for an additional term that in view of this new situation must perhaps be included in their pressure transport Eq. ( 3) to more correctly describe the plasma dynamics, namely a term that describes the change of the electron pressure due to energy that has to be expended by the electrons in order to cause changes in the plasma flow velocity, that is, the ion bulk velocity U(s) along the streamline.…”

“…Therefore, even at the present time there is little observational information available for example about shock-processed pick-up protons and electrons, if not otherwise derivable from independent data. This means that our current understanding of the particular characteristics of this multifluid magnetohydrodynamics (MHD) shock, the thermodynamic essentials, and its internal entropy dissipation is still based on purely theoretical guesses and principles (see early papers by Decker et al 2008;Izmodenov & Baranov 2006;Fahr & Chalov 2008;Wu et al 2009;Zank et al 2010;Chalov & Fahr 2011, and more recent papers by Fahr et al 2015Fahr et al , 2017Chalov 2019a,b;Fahr & Dutta-Roy 2019).…”