In the previous section we discussed models where the net heating efficiency ηnet was fixed at a constant value at all altitudes. In this section we discuss more realistic models of HD209458b that rely on new approximations of photoelectron heating efficiency and derive an estimate of ηnet based on these models. Here we also include radiative cooling from recombination and, in one case, H Lyman α emissions by excited H (Murray-Clay et al., 2009). Our aim was to calculate the most likely range of temperatures in the thermosphere of HD209458b based on average solar fluxes. Fig. 4 shows the temperature and velocity profiles at 1–5Rp based on different approximations (see Table 2 for the input parameters). Model C1 assumes a constant photoelectron heating efficiency of 93% at all altitudes and photoelectron energies. This heating efficiency is appropriate for photoelectrons created by 50 eV photons at an electron mixing ratio of xe = 0.1 (Cecchi-Pestellini et al., 2009). Model C2 is otherwise similar to C1 but the heating efficiency varies with photoelectron energy and altitude (see below). Models C3 and C4 are also based on C1, but C3 includes the substellar tidal forces in the equations of motion (e.g., Garcia Munoz, 2007) and C4 includes Lyman α cooling. All of these models are based on the outflow boundary conditions for temperature, velocity, and density.
Model C1
constant photoelectron heating efficiency
93%
%
photons
50 eV
eV
electron mixing ratio of xe
0.1