Joseph W. Chamberlain

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. Liouvilles 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 Earths 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 Earths 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.

Theory of Planetary Atmospheres: An Introduction to Their Physics and Chemistry

Theoretical models of planetary atmospheres are characterized in an introductory text intended for graduate physics students and practicing scientists. Chapters are devoted to the vertical structure of an atmosphere; atmospheric hydrodynamics; the chemistry and dynamics of the earth stratosphere; planetary astronomy; ionospheres; airglows, auroras, and aeronomy; and the stability of planetary atmospheres. Extensive graphs, diagrams, and tables of numerical data are provided.

A photometric unit for the airglow and aurora

It is suggested that the angular surface brightness B of these sources be measured in units of 106 quanta/cm2 sec sterad. The number quoted should be 4πB, and the unit of 4πB should be called the rayleigh. The advantages of this convention are pointed out and typical values of 4πB for the night and twilight airglow and the aurora are given.

Origin of the sunspot modulation of ozone: Its implications for stratospheric NO injection

Abstract The measured modulation of cosmic rays deposited in the stratosphere over a sunspot cycle produces an oscillating source of stratospheric NO with an 11-yr (quasi) period. The resulting modulation of ozone over this period is calculated and is shown to give good agreement with available measurements of the time lag, the latitude dependence and the magnitude of cyclic variations of ozone. This correlated modulation is then used to discuss the effect on ozone of the injection of NO into the stratosphere from artificial sources, viz. a fleet of supersonic transports and nuclear bomb explosions in the atmosphere.

Resonance scattering by atmospheric sodium—IV abundance of sodium in twilight☆

Abstract The theory of Part I is extended to take account of the hyperfine structure of the D -lines. The absolute intensity of D 1 + D 2 and the ratio D 2 D 1 are computed as functions of total Na abundance for an angle of solar depression, β, of 6·5°. Observations made in Saskatoon are discussed in terms of the seasonal variation of Na. Abundance determinations from the D 2 D 1 ratio in twilight and from the terrestrial component of D -line absorption in the solar spectrum are in good accord with abundances deduced from the absolute twilight intensity.

Excitation of O2 atmospheric bands in the aurora

Abstract Spectra of the aurora show a wide disparity between the rotational temperatures of the two observed Atmospheric bands, b1 Σ +g → X3 Σ −g, with Trot(0–1) ≈ 200°K and Trot(1−1) > 700°K. As the rotational structure of the bands is not resolved, it is not absolutely certain that the temperature anomaly is real, but known features in the auroral spectrum would not produce the effect through blending. Fluorescence in the 0-0 band provides a possible but improbable explanation. Another alternative to explain the data is excitation of O2 by energy transfer from O ( 1 D) (upper term of the red lines) followed by vibrational deactivation. In the latter case the relative intensities of the O2 bands and the [OI] red lines gives an indication of the rate coefficients for the relevant reactions, which are then used to predict the deactivation probability for O ( 1 D) as a function of height. The reactions discussed give a satisfactory explanation of the absence in the airglow of atmospheric O2 bands from vibrational levels v′ ⩾ 1, and predict virtually complete suppression of the [OI] red lines at 100 km in the airglow. The airglow O2 emission gives Trot(0–1) = 183°K,

Depletion of satellite atoms in a collisionless exosphere by radiation pressure

Abstract Hydrogen atoms in Keplerian orbits about a planet are dynamically perturbed by solar Ly α radiation. These perturbations are examined here by analyzing the rates of change of the classical orbital elements, with rather different conclusions from those drawn by Bertaux and Blamont (1973) from numerical integration of sample orbits. There are three main effects: high inclination orbits with eccentricities e ⪆ 0.4 are forced toward the ecliptic plane within a few weeks; the perigees of direct [or retrograde] orbits drift rapidly (i.e., in a few days) toward stable positions roughly westward [or eastward] of the planet; satellite orbits in or near such a stable point rapidly lower their perigees and the satellites life is ended by a collision in the atmosphere. Thus there are effects tending to diminish the number of highly eccentric orbits with distant apogees in all six principal directions (N, S; Sun, anti-Sun; E, W). The various lifetimes are compared for a sample of initial elements.

Eleven-Year Variation in Polar Ozone and Stratospheric-Ion Chemistry

A mechanism for producing an 11-year oscillation in ozone over the polar caps is the modulation of galactic cosmic rays by the solar wind. This mechanism has been shown to give the observed phase in ozone oscillations and the correct qualitative dependence on latitude. However, the production of nitrogen atoms from cosmic-ray collisions seems inadequate to account for the ozone amplitude. Negative ions are also produced as a result of cosmic-ray ionization, and negative-ion chemistry may be of importance in the stratosphere. Specifically, NOx– may go through a catalytic cycle in much the same fashion as NOx, but with the important distinction that it does not depend on oxygen atoms to complete the cycle. Estimates of the relevant rates of reaction suggest that negative ions may be especially important over the winter polar cap.

Resonance scattering by atmospheric sodium—I: Theory of the intensity plateau in the twilight airglow

Abstract Chandrasekhar s theory of radiative transfer is applied to the twilight airglow. The theory, which in most applicable to the region of the intensity plateau, is developed for comparison with measurements of the absolute brightness, the variation of brightness during twilight, and the intensity ratio D 2 D 1 , to obtain the number of Na atoms per cm2 (column). Numerical results are presented for a layer scattering solar D-line radiation and observed in the zenith or at zenith distance 75°. The effect of diffuse reflection of the D lines by the ground is also evaluated approximately. Some of Huntens observations during winter give absolute brightnesses that are slightly greater than the maximum values predicted by the theory. Means of reconciling this discrepancy are discussed. It is tentatively concluded on the basis of theory-observation comparisons that the abundance of Na varies between 109 (summer) and nearly 1010 (winter) atoms/cm2 (column). It is suggested that the D 2 D 1 ratio may be the most reliable means of determining winter-time values of the abundance.

The origin of nitrogen ionization in the upper atmosphere

Abstract Although the N 2 + First Negative bands in twilight are probably the result of resonance scattering by N 2 + ions, the symmetry of morning and evening observations make it unlikely that the ionization is produced by sunlight in the E -region. If the flux in the He II λ304 line is as high as 15 erg cm −2 sec −1 , the observed First Negative system intensities can be accounted for, and the nitrogen ionization is localized in the F -region. If the flux in the λ304 line is much smaller, the ionization must be produced by incident charged particles in the E -region.