Using kappa functions to characterize outer heliosphere proton distributions in the presence of charge-exchange

Kappa functions have long been used in the analysis and modeling of suprathermal particles in various space plasmas. In situ observations of the supersonic solar wind show its distribution contains a cold ion core and power-law tail, which is well-represented by a kappa function. In situ plasma observations by Voyager, as well as observations of energetic neutral atom (ENA) spectra by the Interstellar Boundary Explorer (IBEX), showed that the compressed and heated inner heliosheath (IHS) plasma beyond the termination shock can also be represented by a kappa function. IBEX exposes the IHS plasma properties through the detection of ENAs generated by charge-exchange in the IHS. However, charge-exchange modifies the plasma as it flows through the IHS, and makes it difficult to ascertain the parent proton distribution. In this paper we investigate the evolution of proton distributions, initially represented by a kappa function, that experience losses due to charge-exchange in the IHS. In the absence of other processes, it is no longer representable by a single kappa function due to the energy-dependent, charge-exchange process. While one can still fit a kappa function to the evolving proton distribution over limited energy ranges, this yields fitting parameters (pseudo-density, pseudo-temperature, pseudo-kappa index) that depend on the energy range of the fit. We discuss the effects of fitting a kappa function to the IHS proton distribution over limited energy ranges, its dependence on the initial proton distribution properties at the termination shock, and implications for understanding the observations.