would have condensed and poured down as hot rain, perhaps at the torrential rate of about a meter a day. As the silicates rained out, gaseous compounds—especially CO2, CO, H2O, and H2 but also nitrogen, the noble gases, and perhaps moderately volatile elements, such as zinc and sulfur—would become increasingly prominent.
How the transition from a hot, mostly molten mantle to something more akin to Earth’s current structure happened and how fast are still matters of debate. The cooling of a “magma ocean” is a complex process, with significant uncertainties regarding the material properties of the molten and semimolten silicates, the efficiency of gas exchange between a magma ocean and the atmosphere, how much of which gases were available, and the effects of tidal heating from the Moon. We know from experiments that molten silicate would start to crystallize when the surface temperature dropped to about 1700 K and would be completely solid at about 1400 K. According to one model (Figure 1.9), the surface magma could have cooled enough for crystals to start forming after about 1,000 years and then become completely solid after about 2 million years (Zahnle, 2006). During the cooling period, most of the water and CO2 held in solution in the magma ocean could have been vented to the atmosphere.
According to this model, solidification of the magma ocean would have taken as long as 2 million years because heat escaping from the surface would have triggered a “runaway” greenhouse state in the atmosphere, slowing the rate of heat loss (see Box 1.3). Tidal heating of Earth by the Moon would also have slowed cooling of the magma ocean (Zahnle et al., 2007). Just after its formation the Moon was much closer to Earth (perhaps half the distance) and its tidal force was much stronger than it is now. When the mantle was still completely molten, the tidal heating would have been relatively weak, but because tidal heating is concentrated wherever the mantle is solid, it would have tended to prevent the mantle from freezing.
The resultant slow cooling of the magma ocean could, in turn, have influenced the Moon’s distance from Earth, which would explain why the Moon’s orbit is tilted relative to Earth’s orbit around the Sun (Touma and Wisdom, 1998). The relationship between the Moon’s orbit and the magma ocean is somewhat complicated, but in essence the Moon could move
Runaway Greenhouse Effect
The runaway greenhouse effect is usually encountered as the culprit in textbook accounts of how Venus lost its water. In essence, there is an upper limit on how much thermal radiation can be emitted by an atmosphere in equilibrium with liquid water. This upper limit is called the runaway greenhouse limit, and it is about 310 W/m2 for the modern Earth (Abe, 1993). If the planet absorbs less solar energy than the runaway greenhouse limit, all is well: the climate settles into a stable balance between photons absorbed and photons emitted. But if the planet absorbs more solar energy than the runaway greenhouse limit, the planet cannot balance its energy budget and its surface heats up. The heating continues until all the water, including clouds, has evaporated. For Earth, total evaporation of all water would leave a deep H2O-CO2 atmosphere over a sea of magma (Zahnle, 2006). Eventually, after some intervening photochemistry and a great deal of time, the hydrogen would be liberated from the water and lost to space. This probably happened to Venus. As our Sun brightens, this too will be Earth’s fate.
For the Hadean Earth a runaway greenhouse state could theoretically coexist with a magma surface provided that sufficient water (at least a tenth of the volume of our current oceans) is present at the surface (Zahnle, 2006). The heat flow required to maintain a runaway greenhouse atmosphere (i.e., the maximum rate of cooling) would be ~150 W/m2. Heat flow on the modern Earth is an average of 0.087 W/m2.
away from Earth only as fast as it could deposit energy into Earth’s mantle by tidal heating. For the Moon to lose energy to Earth’s mantle efficiently, the mantle would have to be solid rather than liquid. Because solidification likely took place slowly, the Moon could drift away from Earth only at an exceedingly slow rate. This slow recession of the Moon would have allowed it to be captured into orbital resonances that gave the orbit the inclination it now has. This seemingly strange relationship between the Moon’s orbit and Earth’s mantle is produced by a fundamental property of planetary interiors—the dependence of viscosity on temperature—which is also critical to understanding why Earth is a geologically active planet (Questions 4, 5, and 6).
We do not know how thick the atmosphere would have been after the silicates vaporized by the Moon-forming