Origin of the discrepancy between energy-flux and ionization-rate crossover distances

Determine whether the discrepancy between the approximately 1.72 au crossover distance obtained from galactic-cosmic-ray and stellar-energetic-particle energy fluxes for K2-18b and the 10 au crossover distance reported for molecular-hydrogen ionization rates arises from using energy flux as a proxy for ionization rate, differences in stellar-wind modeling, or both.

Background

For K2-18b, the paper finds that galactic-cosmic-ray and stellar-energetic-particle energy fluxes become equal at approximately 1.72 au in the absence of a magnetic field. This differs substantially from the approximately 10 au distance at which Rodgers-Lee et al. (2023) found equal molecular-hydrogen ionization rates for GJ 436 b.

The authors identify two possible explanations: energy flux may not provide a reliable proxy for ionization rate, and differences in the implementation of stellar-wind effects may alter the modeled galactic and stellar particle spectra. The paper does not resolve which explanation is responsible or quantify their respective contributions.