Energy Conservation for Stellar Wind Mass-Loading: Atmospheric Ion Escape

We construct an analytical paradigm called ‘Particles in a Box’ to study the interaction between the solar wind and terrestrial ionospheres. Using energy flux conservation, we derive how wind deceleration drives magnetic pile-up and quantify the critical transition between kinetic-energy-dominated (super-Alfvénic) and magnetic-energy-dominated (sub-Alfvénic) regimes. This framework shows that pick-up ion escape rates in super-Alfvénic stellar winds, such as those experienced by the terrestrial planets in the solar system, can be computed solely from upstream parameters: stellar wind velocity, magnetic field strength, and the cross-sectional area of the interaction region. Hybrid modeling-informed cross-sectional areas are combined with the analytical equations to estimate heavy ion escape rates at Mercury, Venus, Earth, Mars, Titan, and Pluto. Comparisons with spacecraft observations show order-of-magnitude agreement, validating the paradigm’s utility for unmagnetized or weakly magnetized bodies. These results indicate that Particles in a Box is a promising approach for understanding ionospheric escape from weakly magnetized planets. While only solar system objects are directly considered in this study, the paradigm may be able to be extended to non-terrestrial exoplanets.