Is the low-energy tail of shock-accelerated protons responsible for over-ionized plasma in supernova remnants?

Over-ionized, recombining plasma is an emerging class of X-ray bright supernova remnants (SNRs). This unique thermal state where the ionization temperature ($T_{\rm z}$) is significantly higher than the electron temperature ($T_{\rm e}$) is not expected from the standard evolution model assuming a point explosion in a uniform interstellar medium, requiring a new scenario for the dynamical and thermal evolution. A recently proposed idea attributes the over-ionization state to additional ionization contribution from the low-energy tail of shock-accelerated protons. However, this new scenario has been left untested, especially from the atomic physics point of view. We report calculation results of the proton impact ionization rates of heavy-element ions in ejecta of SNRs. We conservatively estimate the requirement for accelerated protons, and find that their relative number density to thermal electrons needs to be higher than $5~(T_{\rm e}/{\rm 1~keV})\%$ in order to explain the observed over-ionization degree at $T_{\rm z}/T_{\rm e} \ge 2$ for K-shell emission. We conclude that the proton ionization scenario is not feasible because such a high abundance of accelerated protons is prohibited by the injection fraction from thermal to non-thermal energies, which is expected to be $\sim 1\%$ at largest.