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tokens: wind. Thus, we simulate the transonic hydrodynamic planetary winds. At the Roche lobe height, all simulated atmospheres reach velocities between 10 and 20 km s. 4.2.1. Atmosphere of HD 209458 b First, we focus on the atmosphere of HD 209458 b, which is depicted by the green solid lines in Fig. 5 . Panel a shows how the density decreases from the boundary density of to cm. The extent of the Roche lobe for HD 209458 b is 4.2 above the substellar point and the sonic point is reached at 3.5. The optical depth for EUV photons (60 eV) reaches one at a height of 1.03. This height corresponds well with the atmospheric layer that experiences the maximum volume heating rate. Panel b in Fig. 5 shows that the absorption of XUV emission around the height of 1.03 increases the temperature. This raises the atmospheric scale height and the density gradient becomes more shallow above this height. The temperature reaches a maximum of 9100 K. The bulk velocity strongly increases along with the temperature in the lower atmosphere (see panel c). Panel d shows the net specific radiative heating rate throughout the atmosphere. We plot the specific heating rate, which is the heating rate per gram of material, because it clearly shows where the atmospheric material gains most of the energy for the escape. The net heating rate has a maximum close to the temperature maximum, but declines above 1.6 where the atmosphere is more strongly ionized. There is a distinct dip in the net heating rate at 1.15, which is caused by hydrogen line cooling. This can be seen in panel e, where we show the radiative heating and cooling rates separately as thin, solid lines. Subtracting the radiative cooling rate from the heating rate gives the net radiative-heating rate (solid thick line), which is displayed in panels d and e. Between 1.05 and 1.8 about 45% of the radiative heating produced by the absorption of XUV radiation is counterbalanced by hydrogen line emission, which is mainly Ly cooling. In panel e we further compare the radiative heating rate to the hydrodynamic sources and sinks of internal energy. In the atmosphere of HD 209458 b the advection of internal energy is a heat sink below 1.7, but acts as a heat source above this level, providing 50% of the energy in the upper thermosphere. The adiabatic expansion of the gas is a heat sink throughout the atmosphere. This term stands for the energy, which is converted into gravitational potential and kinetic energy. It now becomes clear why the temperature decreases in the upper thermosphere: Radiative heating becomes inefficient due to a high degree of ionization, but the adiabatic cooling term remains large. Therefore, the advected thermal energy is used to drive the expansion of the gas. Panel e also shows cooling due to thermal conduction, which is largest where the temperature increases most strongly, but it is not relevant in any of the simulations. In Fig. 6 the H+He atmosphere of HD 209458 b is depicted in the middle