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Since the mass loss rates are the function of the mean density of the planetand the stellar irradiation, we calculated about 450 models covering planetswith different densities and stellar irradiation. Our results show that themass loss rates are dependent on the stellar irradiation and the mean density.However, the mass loss rates predicted by the energy-limited equation arehigher than that of hydrodynamic model when the XUV integrated flux is higherthan $\sim$2$\times$10$^{4}$ erg/cm$^{2}$/s. The overestimation can be revisedif the kinetic and thermal energy of the escaping atmosphere is included in theenergy-limited equation. We found that the heating efficiencies areproportional to the product of the gravitational potential of the planet andthe stellar irradiation. The mean absorption radii of stellar irradiation are1.1-1.2 R$_{p}$ for the Jupiter-like planets while they vary in the range of1.1-1.7 R$_{p}$ for the planets with smaller sizes. We evaluated the absorptionof stellar Ly$\alpha$ by planetary atmosphere and found that the deeperLy$\alpha$ absorptions tend to locate in the high stellar irradiation and lowplanetary mean density regions, and vice versa. Moreover, planets with massloss rates higher than 10$^{11} g/s$ are likely to exhibit obvious absorptions.Finally, we suggested that the absorption levels are related to the inherentproperties of the exoplanets. The planets with larger sizes (or lower meandensity) show strong Ly$\alpha$ absorptions. Neptune-like and Earth-likeplanets tend to have weak Ly$\alpha$ absorptions because of their small sizes(or high densities).

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