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 extrosolar planet is presented when the continuity and momentum equations of each component have been already solved with an energy equation. The particle number density, the temperature distribution and the structure of velocity can be found by means of the model. We chose two special objects, HD 209458b and HD 189733b, as discussion samples and the conclusion is that their mass loss rates predicted by the model are in accordance with those of observation. The most important physical process in coupling each component is charge exchange which tightly couples atomic hydrogen with protons. Most of the hydrogen escaping from hot Jupiters is protons, especially in young star-planet system. We found that the single-fluid model can describe the escape of particles when the mass loss rate is higher than a few times $10^{9}$ g/s while below $10^{9}$ g/s the multi-fluid model is more suitable for it due to the decoupling of particles. We found that the predicted mass loss rates of HD 189733b with the assumption of energy-limit are a factor of 10 larger than that calculated by our models due to the high ionization degree. For the ionized wind which is almost compose of protons, the assumption of energy-limit is no longer effective. We 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.