The H/H+ transition in the MC09 model occurs near 1.4Rp. If we replace the gray approximation with the full solar spectrum in this model, the H/H+ transition moves higher to 2–3Rp. This is because photons with different energies penetrate to different depths in the atmosphere, extending the heating profile in altitude around the heating peak. This is why the temperature at the 30 nbar level in the C2 model is 3800 K and not 1000 K. In order to test the effect of higher temperatures in the lower thermosphere, we extended the MC09 model to p0 = 1 μbar (with T0 = 1300 K) and again used the full solar spectrum for heating and ionization. With these conditions, the H/H+ transition moves up to 3.4Rp, in agreement with the C2 model. We conclude that the unrealistic boundary conditions and the gray approximation adopted by Murray-Clay et al. (2009) and Guo (2011) lead to an underestimated overall density of H and an overestimated ion fraction. Thus their density profiles yield a H Lyman α transit depth of the order of 2–3% i.e., not significantly higher than the visible transit depth.
H/H+
transition
near 1.4Rp
Rp
H/H+
transition
2–3Rp
Rp
C2 model
level
30 nbar
nbar
C2 model
temperature
3800 K
K
C2 model
temperature
1000 K.
K
MC09 model
p0
1 μbar
μbar
MC09 model
T0
1300 K
K
H/H+
transition
3.4Rp
Rp
H Lyman α transit depth
2–3%
%