For an isothermal atmosphere with a temperature T0, Eq. (11) reduces to the famous result for the altitude of the sonic point (Parker, 1958):where  is the thermal escape parameter X0 at the lower boundary r0. The isothermal sonic point in the C1 model is located at 7.2Rp where c(ξc) = 7.2 km s−1. The volume averaged temperature of the C1 model below this point is approximately 7100 K. Assuming that r0 = Rp, T0 = 7100 K, and m = mH, X0 ∼ 16 and Eq. (12) yields ξc ∼ 8. In this case the analytic result agrees fairly well with the hydrodynamic model if one accounts for partial ionization of the atmosphere by assuming that the mean atomic weight2 is m = 0.9mH.
C1 model
located at
7.2Rp
Rp
c(ξc)
7.2 km s−1
km s−1
C1 model
volume averaged temperature
approximately 7100 K
K
C1 model
T0
7100 K
K
C1 model
X0
∼ 16
mean atomic weight2
0.9mH
mH