tokens: show that the dependence of the mass loss rates on the EUV SED is mild. Thus, using an arbitrary EUV SED profile provides a reasonable estimation for the mass loss rate. Figure 13. The variations of the total mass loss rate with the variation of spectral index F 50–400 / F 50–900 . The mass loss rates are determined by the amount of effective absorption of stellar EUV radiation. Thus, the heating is related to the product of number densities of species and the absorption cross-sections ( H heat ∼ nσ ν ). High-energy photons can penetrate deeper into the atmosphere due to the smaller cross-sections. In the dense regions of the atmosphere, more species can absorb the stellar irradiation. On the other hand, the regions where low-energy photons are absorbed are at a higher altitude than those where high-energy photons are absorbed. Due to the decrease in the number density of species with increasing altitude, the number of particles absorbing the stellar irradiation also decreases. However, the effective heating by high- and low-energy photons is comparable because the heating of the atmosphere is proportional to the number density of particles and the cross-section of photoionization. For atomic hydrogen, the cross-section of photoionization is inversely proportional to the cube of the frequency (Spitzer 1978 ). This also explains why the total mass loss rates predicted for different EUV spectra are comparable. 4. SENSITIVITY OF ATMOSPHERIC PROPERTIES TO EUV SEDS: DISCUSSION 4.1. The Effect of Hydrodynamic Escape Parameters on the Temperature In Table 2 , we have shown that the hydrodynamic escape parameter (where R p and M p are the radius and mass of the planet, and μ and T 0 are the mean mass per particle and temperature at the lower boundary of the atmosphere) is smaller for Kepler-11b than for other planets. The hydrodynamic escape parameter is defined as the ratio of the potential energy to the kinetic energy of the gas. The gas can be bound to the planet if the temperature of the gas is very low or the radius of the planet is small (the mass of the planet is assumed to be constant). In such a case, the value of λ is large. For higher temperatures and/or larger R p values, however, the kinetic energy of the gas can be greater than the potential energy. Thus, the atmosphere can escape the bounds of the planet. The latter case corresponds to a smaller λ . In an atmosphere heated by XUV radiation of the host star, the temperature of the gas can reach a few thousand kelvin at the bottom of the atmosphere (Yelle 2004 ; Murray-Clay et al. 2009 ; Guo 2011 , 2013 ). Thus, the value of λ can decrease with increasing altitude as a result of high temperatures and a large radius. This means that the gas can escape the planet at some altitudes. The critical value of λ to produce a hydrodynamic wind is about 10–15 (Stone Proga 2009 ). Thus, a thermally driven hydrodynamic wind can be produced easily in the atmosphere with a smaller λ because weak XUV
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