A Self-Consistent Treatment of the Oxygen Dissociation Region in the Upper Atmosphere

Abstract

A self-consistent theory is suggested for the determination of the distribution of atomic and molecular oxygen and the temperature in the region 100-140 km of the atmosphere. It is assumed that solar radiation is responsible for the photodissociation of the oxygen molecules, and that the recombination of the atoms by two-body radiative processes is more important than that by three-body collisions (as justified from theoretical considerations). From the postulated conditions for the steady state, namely, for any given volume, (a) the average time rate of dissociations equals that of recombinations, and (b) the average time rate at which radiation energy is absorbed in dissociation processes equals that at which radiation energy is emitted in recombination processes, together with an appropriate form of the barometric equation, it is possible to obtain the concentrations of the molecular and the atomic oxygen and the temperature, all as functions of height, provided the temperature and its gradient are given at one height. Calculations have been carried out for three sets of these boundary values at 100 km, namely, (i) $T=300$\ifmmode^\circ\else\textdegree\fi{}K, $\frac{\mathrm{dT}}{\mathrm{dx}}=10\ifmmode^\circ\else\textdegree\fi{}$/km, (ii) $T=300$\ifmmode^\circ\else\textdegree\fi{}K, $\frac{\mathrm{dT}}{\mathrm{dx}}=5\ifmmode^\circ\else\textdegree\fi{}$/km, and (iii) $T=270$\ifmmode^\circ\else\textdegree\fi{}K, $\frac{\mathrm{dT}}{\mathrm{dx}}=5\ifmmode^\circ\else\textdegree\fi{}$/km. In all these cases, dissociation begins between the heights 90 and 100 km and is not complete until around 150 km. The total gas pressure for various heights above 100 km calculated for case (iii) above agrees quite well with the data obtained from V-2 rocket flights.In the appendices, three-body recombinations are discussed. The cross section for a three-body recombination process is defined, and its relation with the cross section of its inverse two-body excitation process is obtained on statistical mechanical arguments. Also, the relation between the absorption coefficient for a photodissociation process and the cross section of its inverse radiative recombination process is obtained.