The photodissociation of water vapor, evolution of oxygen and escape of hydrogen in the earth's atmosphere

Citation

Brinkmann, Robert Terry (1969) The photodissociation of water vapor, evolution of oxygen and escape of hydrogen in the earth's atmosphere. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1VBY-7D73. https://resolver.caltech.edu/CaltechETD:etd-10062004-120013

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Previous theoretical studies of the photodissociation of water vapor and the resulting evolution of oxygen in the earth's atmosphere have led to the conclusion that over most of geologic time the atmospheric oxygen abundance has been quite low ([...] times the present atmospheric level). These studies have played a prominent role in subsequent investigations concerning biological evolution, interpretation of the geologic record and the evolution of planetary atmospheres. However, these early studies contain several objectionable features which cast serious doubt on the validity of the results. In particular, the path length dependence of the "effective absorption coefficient" in the Schumann-Runge bands of oxygen has not been properly handled and the calculations have been based on the incorrect assumption that dissocation of H2O can be neglected when its rate is appreciably less than the rate of absorption by O2. When these deficiencies are rectified it appears that, contrary to the previous findings, the O2 level could have reached an appreciable fraction of the present amount in the absence of biological activity. Thus, if the earth's early atmosphere were indeed highly reducing, some other explanation for this fact must be found. One possibility which has been suggested is that very early in the earth's history sufficient quantities of hydrogen were outgassed to raise the thermal conductivity of the upper atmosphere, reduce its temperature and consequently retard the escape of hydrogen atoms. It has been suggested that such a "metastable" atmosphere could have existed for perhaps a billion years. This estimate, however, depends on the efficiency of the gravitational escape of light atoms from a planetary atmosphere, i.e., on the importance of the deviations from Jean's classical escape equation due to the escape-induced departure of the atmospheric atoms' velocity distribution from a Maxwell-Boltzmann law. This problem is too complex to be handled entirely analytically, but the statistical approach seems promising. Indeed, three independent Monte Carlo calculations have been recently conducted. Unfortunately, 1) there are potentially serious errors or unjustified simplifications inherent in all three studies and 2) the results from the three studies are so discordant that even a qualitative idea of the validity of the Jeans escape rate cannot be obtained. In view of the importance of ascertaining the magnitude of the correction to Jeans' equation yet another Monte Carlo study has been conducted. This study differs from previous efforts in many respects, two of which are that accurate angular and velocity dependences have been calculated for the cross-section for the elastic scattering of an H (or He) atom by an 0 atom in the WKB approximation, and that rather than following the particles of the real atmosphere (as did all previous workers), here those particles missing from the real atmosphere by virtue of the escape process have been considered. It is found that only moderate corrections to Jeans' escape rate are needed. No firm picture can be sketched of the condition of the earth's early atmosphere from these considerations. Thus the nature of the evolution of the earth's atmosphere is less well known today than understood.

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