The most basic model for a planet's neutral atmosphere involves assuming hydrostatic equilibrium. This approximation may be expected to fail in regions of the atmosphere where flows are significant; these include regions with (ordinary, water cloud) weather and/or those in which dynamically important turbulence exist, presumably associated with temperature gradients. For future reference we write the momentum equation for a neutral species, from Eq. (3.30), as
where is the acceleration due to gravity and represents the net source/loss of particles. (The last term is a mass-loading term.) In hydrostatic equilibrium the left hand side of (16.1) is zero, whence in the absence of sources and losses
Consider a planar model with the height variable z and anti-parallel to the z axis. Assuming the ideal gas law, then
with H(z) = R T(z) / g, the scale height for the atmosphere. This equation has the exponential solution
Assuming and writing , then
with . That is, the simplest prediction for the atmosphere of a planet or moon is that the density should decrease exponentially with height. These results should be familiar to you, having been derived already in Lectures 6 and 7 for the Sun.
Figure 16.1 [Abell, 1982] shows that the number density of Earth's neutral atmosphere does indeed decrease approximately exponentially with altitude in localized regions.
Figure 16.1: Variations in the density and temperature of Earth's neutral atmosphere with altitude [Abell, 1982].
However, a pure exponential decrease would be a straight line in Figure 16.1 and it is clear that this prediction is not consistent with the observed density profile. The primary reason for the profile being only locally exponential is that the temperature and so the scale height vary with altitude. Where the temperature is reasonably constant, i.e., above 200 km altitude and below about 70 km altitude, the profile is approximately indeed exponential with an approximately straight line in Figure 16.1.
Equation (16.1) also holds individually for multiple separate neutral species. The result that suggests that the atmosphere's composition will vary substantially with height, with more massive species being restricted to low altitudes and light species dominating the atmosphere at large altitudes. While this idea is qualitatively correct, it turns out that Earth's atmosphere is well mixed at altitudes below about 100 km (the homopause), presumably due to the effects of weather and turbulence, while the atmospheric constituents do separate out by mass at higher altitudes. This explains qualitatively why planetary atmospheres are dominated by hydrogen (and associated ions) at large altitudes.
The temperature layers in Figure 16.1 are associated with absorption of solar radiation by particular molecules or atoms. Figure 16.2 describes these layers and the temperature structure in more detail.
Figure 16.2: Regions of the atmosphere and associated variations in temperature [Fix, 1995].
The atomic oxygen diffuses both upwards and downwards. Nitrogen molecules also undergo photodissociation, populating the upper atmosphere with atomic nitrogen and leading to species like NO. The smaller oxygen mass leads to oxygen dominating the atmospheric composition at higher altitudes, before hydrogen dominates at even higher altitudes. Note that N makes up about 78% of the atmosphere by mass, on average.
Figure 16.3: Neutral atmospheric densities for various molecular and atomic species [Cravens, 1997].
and 16.4 indicate the changing nature of the atmosphere above 100 km and the start of the ionosphere.
Figure 16.4: International quiet solar year daytime ionospheric and atmospheric composition based on mass spectrometer measurements [Johnson, 1969; Luhmann, 1995].
These figures also illustrate how dominates the plasma at altitudes from about 150 km to about 600 km, while dominates above about 1000 km. This difference can be important; for instance, the space shuttle encounters primarily an plasma at its altitude km, permitting collisional charge-exchange with water outgassing from the shuttle and causing the shuttle's plasma environment to be filled with pickup ions and associated plasma waves. These figures also illustrate the complicated spatial structure of the ionosphere, as partly forewarned in Figure 16.1.