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The escape of hydrogen-rich atmosphere of exoplanet: Mass loss rates and the absorptions of stellar Lyman $α$

Since the mass loss rates are the function of the mean density of the planet and the stellar irradiation, we calculated about 450 models covering planets with different densities and stellar irradiation. Our results show that the mass loss rates are dependent on the stellar irradiation and the mean density. However, the mass loss rates predicted by the energy-limited equation are higher than that of hydrodynamic model when the XUV integrated flux is higher than $\sim$2$\times$10$^{4}$ erg/cm$^{2}$/s. The overestimation can be revised if the kinetic and thermal energy of the escaping atmosphere is included in the energy-limited equation. We found that the heating efficiencies are proportional to the product of the gravitational potential of the planet and the stellar irradiation. The mean absorption radii of stellar irradiation are 1.1-1.2 R$_{p}$ for the Jupiter-like planets while they vary in the range of 1.1-1.7 R$_{p}$ for the planets with smaller sizes. We evaluated the absorption of stellar Ly$α$ by planetary atmosphere and found that the deeper Ly$α$ absorptions tend to locate in the high stellar irradiation and low planetary mean density regions, and vice versa. Moreover, planets with mass loss rates higher than 10$^{11} g/s$ are likely to exhibit obvious absorptions. Finally, we suggested that the absorption levels are related to the inherent properties of the exoplanets. The planets with larger sizes (or lower mean density) show strong Ly$α$ absorptions. Neptune-like and Earth-like planets tend to have weak Ly$α$ absorptions because of their small sizes (or high densities).