Is it possible to escape from the conclusion that the planetesimals that made the bulk of the Earth were completely outgassed and devoid of any volatiles. Let us consider the chain of arguments in detail.
(a) The cosmothermometer at 2.6 AU is valid. The heterogeneous microscopic composition of the chondrites, combined with their total lack of igneous
Fig. 2.3. This thermochemical equilibrium for carbon compounds, in a gas of solar composition, is used to understand the carbon chemistry in the solar nebula at the time of dust sedimentation. The quasi-vertical curves represent the adiabats of Cameron's (1985) models C and D, whereas curve CD is an interpolation of the two models C and D that brings all temperatures in agreement with those of Fig. 2.2. The different steady-state models C, CD, and D can be interpreted as a slow evolutionary sequence (shown by the arrows) corresponding to the time when the inflow of nebular gas onto the disk is slowly subsiding. This allows gas turbulence to diminish, eventually letting the dust separate from the gas and sediment to the midplane of the disk. Identification with Fig. 2.2 shows that this happens when adiabat CD is reached. Then, dust settles out and is removed from its chemical equilibrium with gas. At the Earth distance (circle with inside cross) this happens near 900 K; chemical kinetics are fast and dust grains are at thermochemical equilibrium with gas before their sedimentation. Beyond 2.6 AU, chemical kinetics prevails at temperatures lower than 450 K; there, metastable carbonaceous compounds separate from the nebular gas and are imprisoned in carbonaceous chondrites. The other lines on the diagram separate the zones; here CO, CH4, CO2, or C (graphite) are each the major constituent. If the conditions of adiabat CD are applicable as implied by Fig. 2.2, then all carbon was in gaseous CO in the Earth zone; carbon on the Earth must be exogenous and must have come later.
differentiation, leaves little doubt that the variable fractionation and loss of their volatile metals date back from their sedimentation as fine dust and is due to a temperature gradient. The temperature separating the two classes is confirmed by several independent comothermometers: the fractionation of the volatile metals (Pb, Bi, Tl, and In) (Larimer, 1967); oxidation state (olivine/pyroxene ratio) (Larimer, 1968); the presence of FeS and the absence of magnetite in carbonaceous chondrites confirms the temperature range (Anders, 1971); even if the Fischer-Tropsch Type (FTT) reactions are no more considered as unambiguous (Kerridge 1991), their possible presence in carbonaceous chondrites would bring only a further confirmation of the 450 K temperature separating the carbonaceous from the ordinary chondrites (Anders, 1971). Finally, there is not much doubt about the identification of the S (stony) asteroids with the ordinary chondrites and the C (carbonaceous) asteroids with the carbonaceous chondrites. If the present 2.6 AU distance had changed somewhat because of mass loss within the solar nebula, the 1 AU distance of the Earth would have shifted in the same proportion and the net result of our computation would be the same. (b) The temperature gradient at sedimentation of dust is not much in doubt, because the theoretical prediction of Morfill's (1988) model is confirmed by the empirical gradient deduced by Lewis (1974); both are close to -1, which is also derived from a simple-minded argument based on the virial theorem. The virial theorem implies that, in the absence of any latent heat (due, for instance, to the condensation of silicates or of water) the temperature gradient is the same everywhere as that of the gravitation potential. This is close to -1 as soon as the mass is concentrated in the Sun.
The virial theorem can be used only if the angular acceleration of the disk is negligible. This is always the case when sedimentation takes place. Besides, the virial theorem tells only how much heat is available from the gravitational collapse; at steady state, the heat reradiated by the disk photosphere depends on its temperature, hence on the radial distance. This explains the corrected gradient of -0.9 introduced in Morfill's approximation.
Wood and Morfill (1988) also discuss simplified models of the three major stages of the accretion disk. Their stage 1 describes the period during which the disk mass is steadily increasing; it is irrelevant for our concern. Their stage 2 describes the epoch when the rate of inflow equals the mass rate fed to the Sun. During this steady state, the temperature gradient in the midplane of the disk is -1.5. Stage 3 is reached when the infall rate diminishes enough to stop the gas turbulence; the disk still feeds the Sun until its mass diminishes enough to make it transparent. At that time, the temperature gradient in the midplane has fallen down to -0.75. Since the sedimentation of dust is triggered by the disappearance of gas turbulence, the temperature gradient in the midplane falls down slowly from -1.5 to
-0.75. This is consistent with the empirical value close to -1 for the epoch of separation of dust from the gas. See also Lin and Papaloizou (1985). Cassen et al. (1985) have also compared the temperature distribution at different stages. They find that the photospheric temperature has a radial gradient of -0.75 regardless of the details of the viscous mechanism. However, when the disk is optically thick, its opacity implies that the midplane temperature remains closer to the results of the virial theorem, hence this remains consistent with the Morfill's (1988) temperature gradient of -0.9 in the midplane. We conclude that the consensus between theory data and empirical data is satisfactory.
(c) At sedimentation, the mean temperature of earthy dust is high enough to degass it. After sedimentation, earthy dust was on circular orbits located between 0.8 and 1.3 AU. Dust grains started to stick together, and their sizes grew slowly. After a few thousand years, they had become large enough to be called planetesimals, and the eccentricities of their orbits started to grow steadily, in step with their growing sizes (Wetherill, 1980). As seen on Fig. 2.2, their accretion temperatures were at least 800 K, even if the least steep gradient of -0.9 is used. The limiting gradient of -0.75 (which would yield 700 K for the coolest grains) is ruled out before the grains are imprisoned in meter-sized bodies; and even 700 K would outgas the grains.
Of course, we deal with a stochastic process; this means that, in the very final steps of accumulation, some of the major collisions with lunar-sized planetary embryos could come from objects whose initial heliocentric distance of accumulation were outside our definition of the Earth's zone (0.8-1.3 AU). An object that accumulated in a zone nearer to the Sun would be even more outgassed than the protoearth; but if a large embryo were coming from the inner asteroid belt (2.0-2.6 AU), it could bring ordinary chondritic material to Earth. Such a possibility was ruled out until recently, because it was believed that no object ever became larger than Ceres in the asteroid belt. However, Wetherill (1991) has shown by numerical Monte-Carlo experiments that it is conceivable that larger runaway embryos could have formed in the asteroid belt, then ejected later by Jupiter secular resonances. The self-clearing of the inner belt is assisted by collisions with terrestrial planets. However, the process induces higher eccentricities and inclinations than those observed for the terrestrial planets. Such a collision, which would not greatly change the orbit of the Earth, is a grazing collision, which seems more proper to explain the origin of the Moon (Cameron, 1988) without depositing volatile material deep into the Earth's mantle.
(d) The chemistry of the solar nebula is reasonably well understood, including its chemical kinetics (Prinn and Fegley, 1989). The fact that FTT reactions are likely beyond 2.6 AU, and that there is kinetic inhibition in the vapor-phase hydration of the silicates as well as in the chemical reduction for CO and N2 does not change the conclusions that the chemical equilibrium was virtually reached in the Earth's zone (0.8-1.3 AU). The only possible exception is that of many minor metastable phases in the solid grains dating back from interstellar space, like submicrometer diamonds, fullerene balls, or large polyaromatic hydrocarbon molecules. The rest of all carbon was entirely in gaseous CO, except another very minor fraction in solid solution in reduced (metallic) iron grains. In the same way, all nitrogen was in gaseous N2 and all water was in steam. No water, no nitrogen, and no organic carbon to speak of, were present in the protoearth.
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