PLANETARY CORONAE AND ATMOSPHERIC EVAPORATION

A comprehensive theory is presented for the region of a planetary atmosphere where collisions are rare and where the controlling factors are gravitational attraction and thermal energy conducted from below. Although the subject of this article originated literally with the kinetic theory itself, until recently attention has been confined to atmospheric evaporation. The early sections (1–4) are developed on the classic assumption of a sharply defined critical level, above which the atmosphere is completely free of collisions. Throughout, the different types of particle orbits are treated separately; coronal particles are either ballistic (meaning captive particles whose orbits intersect the critical level), satellite (captive particles orbiting above the critical level), or escaping. Liouville's equation leads to exact expressions for the density distributions and escape flux. The latter is a simple analytic expression, but the density integrals are more complex and numerical evaluations have been provided in tables. At large distances from the planet all the integrals may be evaluated in their asymptotic limits. Expressions are given for the different density components, the kinetic temperature, and heat flux. The latter two cannot generally be evaluated with the thermal conductivity as normally computed. The integrated density in a column above a specified height and orientated in a specified direction is given particular attention, because it fixes the critical level and because it is essentially an observable quantity. Numerical calculations are given for relating such observations in either the radial or transverse directions to the basic parameters of the corona (the criticallevel density, temperature, and height above the planet). The radial integrated density at the critical level is shown to deviate sensibly from the simple expression applicable to a planeparallel atmosphere unless the gravitational energy is very much greater than the mean thermal energy. Section 5 utilizes results of the preceding theory to justify the adoption in the first place of the concept of a critical level. The principal question focuses on the outward flux of escaping particles. A detailed treatment of escape as governed by collisions agrees with earlier similar analyses in showing that (with certain approximations) the critical-level concept predicts the accurate flux. However, it is noted that this result, except for confirming the height of the critical level, is trivial: it is a consequence of an assumed Maxwellian distribution and the special properties accruing to it. Section 6 treats a variety of related problems dealing with production and loss mechanisms, after some orbital properties and flight times are investigated. The critical-level theory cannot cope with the important question of the abundance of satellite orbits. Here it is shown that the satellite contribution may be included throughout the theory by omitting the expressions for the satellite component as such and evaluating the ballistic component, not with the critical level, but with a higher satellite critical level instead. For the Earth's hydrogen corona this level is near 2.5 Earth radii. The effect of photoionization on the density distribution of escaping orbits is also treated and shown to be negligible for the Earth. The concentration of hot interplanetary gas around a bare planet offers an interesting effect in that screening of orbits by the planet may more than counteract condensation due to the gravitational attraction. A hot, stationary interplanetary gas intermingled with a planetary corona will not have any appreciable effect on the coronal density or temperature distributions. Specifically, it is inappropriate to regard heat as being “conducted” (in the usual meaning of the word) from the interplanetary medium through the corona. Doppler profiles of coronal particles in a column along a specified direction have been examined in Section 7. Asymptotic expressions are given along with the general formulae, which will have to be evaluated numerically if and when the pertinent spectral observations are made. Even at large distances from the planet where the population consists largely of escaping particles, the shape of the spectral profile does not deviate very seriously in radially outward velocities from the profile with the Maxwellian distribution at the critical level. Section 8 examines the basic assumption of the entire preceding theory: the establishment of a Maxwellian distribution near the critical level. The collision treatment here is based on the Boltzmann equation, and while it is crude, it is not trivial. The conclusion is that the Maxwellian distribution in the upward direction is depleted beyond the escape velocity by several per cent, but this depletion is generally negligible when compared with errors produced by small uncertainties in temperature. The deviations would be important only were it possible to make measurements affected by the detailed shape of the velocity distribution curve. Real coronae are summarized briefly in Section 9. While more and better observations are needed, it appears now that the hydrogen geocorona may become seriously perturbed into a geocoma, as Brandt labelled it, by solar particles flowing past the Earth. Attention is also directed to observations of the helium geocorona as a means of clarifying the now highly confused “helium problem”. Some estimates of the features of the Martian oxygen corona are made. Venus, as the Earth's sister planet, is an enigma, but coronal observations may point the way to an explanation of the distinctive differences between the evolution of the atmospheres of Venus and the Earth.