Jeans escape

So far we discussed the case for 4He escape. 3He escape must at least be as effective as 4He the 4He lifetime against Jeans escape can be shown to be 70 times greater than the 3He lifetime. In the case of 4He, an inflow flux into the atmosphere is essentially the radiogenic 4He from the solid Earth. However, a flux from the interplanetary space may become important in the case of 3He inventory. From He implantation experiment on metal foil collectors in the Skylab, a spacecraft operated in a circular orbit at the altitude of 443 km from 1973 to 1974, Lind, Geiss, and Stettler (1979) concluded that the solar wind 3He precipitating from the magnetosphere to the upper atmosphere is comparable to 3He degassing flux from the solid Earth. 

Jeans escape — the process associated with the planetary loss of those molecules to space that have velocities exceeding y/2gr, where g is the planet s gravitational acceleration and r is the distance to the planet s center. 

Measurements of atmospheric water vapor on Mars have found D/H values —5 times that of the Earth and have been fractionated due to Jeans escape of hydrogen to space (Owen et al., 1988), and 2-5 times the terrestrial value in SNC meteorites (Watson et al., 1994). Morphological data (Carr, 1986) and modeling of hydrogen atmospheric losses (Donahue, 1995) suggest that originally there may have been the equivalent of up to 500 m of water, or —7 X 10 g H2O. The total mass of Mars is 0.11 times that of the Earth, and so both planets originally may have had similar bulk water concentrations. 

Values derived from the noble gases on Earth are entered in column three of Table 12-3. It is then easy to see that the deficiency increases toward the lighter noble gases. If this feature is interpreted to have resulted from Jeans escape, one finds that the mass of the body from which the escape took place must have been 100 times smaller than that of the present Earth, provided unreasonably high temperatures are excluded. The result may be used to support the argument that any primordial atmosphere that Earth might have had was removed before Earth had agglomerated to its present size. 

Fig. 12-3. Steady-state concentrations of N2, C02, CO, 02, H2, O, and OH in the prebiotic primitive atmosphere, according to model calculations of (Casting et al. (1979). These authors assumed a steady flux of H2 of 1012 m 2s 1 through the atmosphere, entering it by volcanic exhalations and leaving by Jeans escape.

In discussing Jeans escape of hydrogen generated by the photodissociation of water vapor, we reiterate that the escape rate is determined by eddy diffusion of hydrogenous compounds in the region below the homopause. 

CDrg h2o co2+h2o ch2o+o2 H20 j02 + h2 10 1.2 32.0 1.9 Photosynthesis and burial in the sediments from Table 11-1. Jeans escape of hydrogen, present rate... 

Thermal escape, Jeans escape if we assume that the individual molecules are Maxwellian distributed, then molecules from the high tail of this distribution can escape, if at a given level in the atmosphere the mean free path is comparable to the scale height. According to Maxwell s distribution, the kinetic energy of the molecules depends on the mass and velocity (which depends on the temperature in the atmosphere) ... 

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