Rock Vapor

Panel (a) of Fig. 7.5 begins at this point. The rock vapor atmosphere radiates to space with an effective temperature of order 000 K. The saturation vapor pressure of rock is sensitive to temperature, and therefore the cloudtop temperature is relatively insensitive to details.

The high radiating temperature demands rapid condensation and corresponding very strong updrafts. In addition to the updrafts associated with weather, there is a net updraft of w = 0.4 (Trad/2000 K)4 (p/60 bars) cm/s below the photosphere, driven by silicate condensation (assumes a latent heat of condensation of 1.4 x 1011 ergs/g for silicates). This gets large at low pressures. One speculates that local, weather-driven velocities may approach the sound speed, given the enormous energy fluxes present.

These winds must strongly influence the pressure level and droplet size at the cloudtops. Rayleigh-Taylor instability suggests that liquid drops get no larger than T/gpdmp ^0.2 cm (radius), for reasonable surface tensions of silicate drops in a silicate vapor, where T is the surface tension and g the acceleration (we have assumed that surface tensions of silicates in a silicate vapor are ^100 dynes/cm, a few-fold smaller than what they are in air (Walker and Mullins, 1981)). When unstable, the hydrodynamic instabilites have fast growth rates on the order of 10 s_1. Comparing terminal velocity for 0.2-cm drops to the updraft velocity suggests that rock rain can fall at pressures above (altitudes below) ~0.1 bars. At higher altitudes, solitary drops cannot get big enough to fall; they must be transported by convective eddies, freeze (hailstones), or fall collectively. Silicates vary in their triple point pressures. Some have a much stronger preference to be liquid than water. We speculate that the photosphere is defined by a mist of wind-whipped, wind-sheared spray, the size of the drops determined by the aerodynamic accelerations.

As an illustrative example, consider cloudtops in which 0.1% of the mass is condensed as 100-^m droplets. Such a cloud becomes optically thick at 40 mbars, comparable to the altitude where raindrops can get large enough to fall. The saturation vapor pressure of a mixture of forsterite (Mg2SiO4) and

Fig. 7.5. History of an ocean vaporizing impact. (a, b) An impact on this scale produces about 100 atmospheres of rock vapor. Somewhat more than half the energy initially present in the rock vapor is spent boiling water off the surface of the ocean, the rest is radiated to space at an effective temperature of order 2,300 K. (c) Once the rock vapor has condensed the steam cools and forms clouds. (c, d) Thereafter cool cloudtops ensure that the Earth cools no faster than the runaway greenhouse threshold, with an effective radiating temperature of order 300 K. In the minimal ocean vaporizing impact the last brine pools are evaporated as the first raindrops fall. For somewhat larger impacts a transient runaway greenhouse results, with the surface temperature reaching the melting point.

Fig. 7.5. History of an ocean vaporizing impact. (a, b) An impact on this scale produces about 100 atmospheres of rock vapor. Somewhat more than half the energy initially present in the rock vapor is spent boiling water off the surface of the ocean, the rest is radiated to space at an effective temperature of order 2,300 K. (c) Once the rock vapor has condensed the steam cools and forms clouds. (c, d) Thereafter cool cloudtops ensure that the Earth cools no faster than the runaway greenhouse threshold, with an effective radiating temperature of order 300 K. In the minimal ocean vaporizing impact the last brine pools are evaporated as the first raindrops fall. For somewhat larger impacts a transient runaway greenhouse results, with the surface temperature reaching the melting point.

silica at T « 2,000 K can be approximated by (Mysen and Kushiro, 1988)

The vapor consists mostly of Mg, SiO2, SiO, and O2, with a mean molecular weight of ^40. The scale height at 2,500 K is ~ 50 km. Equation (7.16) implies a temperature at 40 mbars of 2,500 K. If the droplets were increased to 1 mm, the saturation vapor pressure at optical depth unity would rise to 0.4 bars and the temperature to 2,700 K; if the mass fraction in condensates were increased to 1% or the droplets shrunk to 10 |m, the saturation vapor pressure at optical depth unity would fall to 4 mbars and the temperature to 2,300 K.

Even radiating as a 2,300 K blackbody, it would take a few months to radiate away the energy (> 1035 ergs) initially present in the rock vapor. At least as much energy is radiated down onto the oceans as is radiated directly to space, because the temperature at the bottom of the atmosphere will be higher than at the top. The high opacity of seawater to infrared radiation (Suits, 1979) concentrates radiative heating in a thin surface layer. Boiling is confined to this layer. In a sense, thermal radiation from the rock vapor ablates the surface of the ocean, leaving the ocean depths cool. The depth of the boiled layer is determined by compositional convection; the hot but extremely saline surface waters mix with enough of the relatively cool and less saline waters below to leave the surface waters at worst neutrally bouyant. In general, the density decrease from thermal expansion outweighs the density increase from higher salinity, so that boiling is limited to surface waters. This is described in more detail in the first edition of this book (Zahnle and Sleep, 1997).

Just above the surface there is a thin boundary layer where the temperature rises rapidly from the relatively cool boiling waters at the surface to the much hotter rock vapors above. Since water vapor is somewhat transparent to > 2, 000 K thermal radiation (Kasting, 1988), the oceans are not effectively shielded from the hot rock above; yet the water vapor is sufficiently opaque that it is quickly heated to the atmospheric temperature. Once heated the bouyant water vapor rises through and mixes with the denser rock vapor, stirring and homogenizing the atmosphere. The atmosphere is doubtless vigorously convective, driven at the top by radiative cooling at the cloudtops and at the bottom by rising plumes of low density, water-rich gases. The temperature profile is effectively set by the saturation vapor pressure of rock. For a 60-bar rock vapor atmosphere, Eq. (7.16) implies a temperature near the surface of ~3, 400 K. The radiative heat flux onto the oceans exceeds that to space by a factor of order (3400/2300)4 — 5. This factor applies only to the oceans. On dry land the surface quickly heats to reach radiative equilibrium, and rocks begin to selectively melt and evaporate. As the oceans shrink, the relative importance of radiation to space grows. While the oceans remain, most of the energy in the atmosphere goes to evaporating sea water and heating water vapor. To evaporate and heat water vapor to 3,400 K takes some 8.2 x 1010 ergs/g; to do this to the oceans requires ~1.2 x 1035 ergs (This would require an impact times bigger than the minimal ocean vaporizing impact that we have been considering.) At an effective radiating temperature of 3,400 K, the cooling time of the atmosphere reduces to about a fortnight. The actual cooling time would be somewhere between a fortnight and a few months, depending on the relative surface areas of dry land and open seas.

Throughout this period a hot rock rain or hail falls into the ocean at a rate of meters per day. In the minimal ocean-vaporizing impact 200 m of precipitated rock eventually accumulate on the ocean floor. The thermal energy in the rain is considerable. The rainout of a 60-bar rock vapor atmosphere delivers about 1 x 1034 ergs, or roughly 20% of the energy assumed initially present in the ejecta. The raindrops are quenched near the surface, and so contribute to boiling (with a thermal diffusivity k = 0.01 cm2/s it takes about a second to cool a millimeter-size drop and about a minute to cool a centimeter-size drop).

Other heat sinks are probably unimportant. It takes less than 2 x 1032 ergs to heat a 1 bar N2 atmosphere to 3,500 K. Even a 60-bar CO2 atmosphere (if all the CO2 in all the Earth's carbonates were put into the atmosphere) requires less than 1034 ergs to reach 3,500 K. In all likelihood the preexisting atmosphere is quickly raised to the temperature of the rock vapor, either by radiative heating or by mixing with the rock vapor.

The heat capacity of the crust on a timescale of months is also limited because the depth of heating is limited by thermal conduction. The problem is somewhat akin to ablation of meteors. Exposed surfaces would melt and flow downhill, exposing fresh rock. Low spots would also accumulate rock rain at a rate of meters per day. We expect that the net effect is that the original surface would heat to a depth comparable to the 200-m thickness of the ejecta blanket. Assuming a heat capacity of 1.4 x 107 ergs/g/K and a heat of fusion of 4 x 109 ergs/g, and an exposed surface covering 40% of the globe, the crust would absorb about 3 x 1033 ergs while heating to 1,500 K. This is small compared to the energy released by the impact.

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