Constraining the Evolution of the Proton Distribution Function in the Heliotail

We use Interstellar Boundary Explorer (IBEX) measurements of energetic neutral atoms (ENAs) to constrain the proton (mostly pickup ion, PUI) distribution in the heliotail. In our previous study, we solved the Parker transport equation and found that the velocity diffusion coefficient D(v) for PUIs is approximately D(v) ∼ 1.1 × 10^-8 km² s^-3 (v/v ₀)^1.3, assuming the initial proton distribution processed by the termination shock (TS), f _p,0, is a kappa distribution with kappa index κ _p,0 = 1.63. In this study, we test different forms for f _p,0. We find that if f _p,0 is kappa-distributed and D(v) = D ₀(v/v ₀)^1.3, any kappa index in the range 1.5 < κ _p,0 < 10 is consistent with IBEX data if D ₀ ∼ 0.8-1.3 × 10^-8 km² s^-3. While the case where D(v) ∝ v ^1.3 yields ENA fluxes that appear to best reproduce IBEX data for any κ _p,0, it is possible for D(v) to scale close to ∼v ^2/3 or ∼v ² within our uncertainties by changing D ₀. We also show that an upstream PUI filled-shell distribution that is heated by a quasi-stationary TS, generating a downstream filled-shell with large cutoff speed, yields an excess of ENAs >2 keV compared to IBEX. However, using a fully kinetic particle-in-cell simulation to process a PUI filled-shell across the TS yields ENA spectra consistent with IBEX, reinforcing the significance of self-consistent, preferential PUI heating and diffusion at the TS. Interestingly, an upstream PUI distribution inferred from the particle-in-cell simulation to reproduce Voyager 2 observations of the nose-ward TS is inconsistent with IBEX observations from the heliotail, suggesting differences in the upstream PUI distribution or TS properties.