Spectral Evolution of Pickup Ions across Interplanetary Shocks in the Outer Heliosphere: Observational Constraints and Transport Simulations

Pickup ions (PUIs) often experience acceleration and heating as they traverse interplanetary shocks, leading to the formation of a distinct suprathermal tail in their energy spectra downstream of the shock. Combining in situ observations and numerical simulations, we investigate how interplanetary shocks shape the energy spectra of PUIs in the outer heliosphere. In this study, we propose a PUI velocity distribution model by incorporating a power-law tail to account for suprathermal ions. By analyzing 18 shock events observed by New Horizons between 20 au and 45 au, we find that, after crossing the shock, the power-law index η of the suprathermal PUI energy spectrum decreases, and this decrease is positively correlated with the shock compression ratio r c and the downstream subadiabatic index β d . To explore the acceleration mechanism of PUIs, we conduct numerical simulations of the shock transport equation, which incorporates the three acceleration-related mechanisms (shock drift acceleration, diffusive shock acceleration, and stochastic acceleration). Our simulations show that when the perpendicular mean free path of PUIs is within 10 −3 ∼ 10 −2 au and the velocity diffusion coefficient is within 10 −9 ∼ 10 −8 s −1 , the shock transport model can reproduce energy spectra consistent with observations. Both the observed and simulated suprathermal power-law spectra exhibit a steeper spectral profile than predictions from first-order Fermi shock acceleration theory. Most PUIs cross the shock less than three times, resulting in low acceleration efficiency, mainly due to weak spatial and velocity diffusion.