On the evolution of the κ distribution of protons in the inner heliosheath

Abstract

The evolution of the solar wind proton distribution function along the plasma flow downstream of the heliospheric termination shock is studied. Starting from a kinetic phase space transport equation valid in the bulk frame of the plasma flow that takes into account convective changes, cooling, velocity diffusion, and charge exchange-induced injection and loss, the associated moment equation for the evolution of the pressure of the total proton population consisting of thermal solar wind and suprathermal pickup protons is derived. Assuming that the local joint proton distribution can always be represented by a so-called κ distribution, an ordinary differential equation for the variation of the parameter κ along a given streamline is obtained. This way, the proton velocity distribution can be computed for the whole inner heliosheath. It is demonstrated that the accelerating effect of velocity diffusion is to be expected to overcompensate the loss effect on the proton distribution at higher velocities due to charge exchange with cold interstellar hydrogen atoms. While this corroborates a value of κ < 1.65 in the inner (upwind) heliosheath, at the same time it reveals that the assumption of a constant κ, which was commonly made in earlier studies, should be abandoned.