Escaping Particle Fluxes in the Atmospheres of Close-in Exoplanets. I. Model of Hydrogen

A multi-fluid model for an atomic hydrogen-proton mixture in the upper atmosphere of an extrasolar planet is presented when the continuity and momentum equations of each component have already been solved with an energy equation. The particle-number density, temperature distribution, and structure of velocity can be found by using the model. I chose two special objects, HD 209458b and HD 189733b, for discussion and concluded that their predicted mass-loss rates are consistent with those observed. The most important physical process in coupling each component is the charge exchange, which couples atomic hydrogen tightly with protons. Most of the hydrogen escapes from hot Jupiters as protons, especially in the young star-planet system. I found that the single-fluid model can describe the escape of particles when the mass-loss rate is higher than a few times 10⁹ g s^-1, while below 10⁹ g s^-1 the multi-fluid model is more suitable because of the decoupling of particles. Assuming an energy limit, I found that the predicted mass-loss rates of HD 189733b are a factor of 10 larger than those calculated by my models because of a high degree of ionization. For ionized wind, which is mainly composed of protons, assuming an energy limit is no longer effective. I fitted the mass-loss rates of the ionized wind as a function of F _UV by calculating the variation of the mass-loss rates with UV fluxes.