Transonic Hydrodynamic Escape of Hydrogen from Extrasolar Planetary Atmospheres

Hydrodynamic escape is an important process in the formation and evolution of planetary atmospheres. Transonic steady state solutions of the time-independent hydrodynamic equations are difficult to find because of the existence of a singularity point. A numerical model is developed to study the hydrodynamic escape of neutral gas from planetary atmospheres by solving the time-dependent hydrodynamic equations. The model is validated against an analytical solution of the escape from an isothermal atmosphere. The model uses a two-dimensional energy deposition calculation instead of the single-layer heating assumption, which is not sufficiently accurate for hydrodynamic escape from a hydrogen-rich planetary atmosphere. When applied to the atmospheres of extrasolar planets, the model results are in good agreement with observations of the transiting extrasolar planet HD 209458b. The model predicts that hydrogen is escaping from HD 209458b at a maximum rate of 6 × 10¹⁰ g s^-1. The extrasolar planet is stable under the hydrodynamic escape of hydrogen. The rate of hydrogen hydrodynamic escape from other possible extrasolar planets is investigated using the model. The importance of hydrogen hydrodynamic escape for the long-term evolution of extrasolar planets is discussed. Simulation shows that through hydrodynamic escape of hydrogen, a planet at the orbit of Mercury (0.4 AU) and with 0.5 Uranus mass can lose about 10% of its mass within 850 million yr if the solar EUV radiation is 10 times the present level. This calculation provides an indication of how Mercury may have evolved during the early days of the solar system.