Origin of the atmospheres of the terrestrial planets

ICARUS 56, 195-201

(1983)

Origin of the Atmospheres of the Terrestrial Planets 1 A. G. W. C A M E R O N Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138

Received February 18, 1983; revised July 14, 1983 The monotonic decrease in the atmospheric abundance of 36Ar per gram of planet in the sequence, Venus, Earth, and Mars has been assumed to reflect some conditions in the primitive solar nebula at the time of formation of the planetary atmospheres, having to do either with the composition of the nebula itself or the composition of the trapped gases in small solid bodies in the nebula. Behind such hypotheses lies the assumption that planetary atmospheres steadily gain components. However, not only can gases enter atmospheres; they may also be lost from atmospheres both by adsorption into the planetary interior and by loss into space as a result of collisions with minor and major planetesimals. In this paper a necessarily qualitative discussion is given of the problem of collisions with minor planetesimals, a process called atmospheric cratering or atmospheric erosion, and a discussion is given of atmospheric loss accompanying collision of a planet with a major planetesimal, such as may have produced the Earth's Moon. m a y act as a tracer. On a gram 4°Ar per gram planet basis, Venus is lower than the Recent m e a s u r e m e n t s o f the a b u n d a n c e s Earth by a factor 4 and Mars is lower than of 36Ar in the a t m o s p h e r e s of the terrestrial the Earth by a factor 16 (Pollack and Black, planets have shown t h e m to be, in gram 1982). The simplest interpretation is that 36Ar per gram planet 2.5 x 10 -9 for Venus, the other planets h a v e outgassed m u c h less 3.5 × I0 -~l for Earth, and 2.1 x 10 -13 for than the Earth. H o w e v e r , a t m o s p h e r i c eroMars (for a review see Pollack and Black, sion by impact o f planetesimals m a y h a v e 1982). This result has been a s s u m e d to re- played a significant role in the case of Mars. flect some conditions in the primitive solar F o r Mars, the time required to eliminate nebula at the time o f formation of the plane- orbit-crossing planetesimals by collision tary a t m o s p h e r e s , having to do either with (collisional lifetime) is m u c h longer than is the composition of the nebula itself or the the case for Venus and the Earth, and atcomposition o f the trapped gases in small mospheric erosion by collisions with these solid bodies in the nebula (Pollack and planetesimals m a y extend into the 4°At outBlack, 1979; M c E l r o y and Prather, 1981; gassing era. Wetherill; 1981). Behind such h y p o t h e s e s Another possible m e c h a n i s m for loss of lies an assumption that planetary atmo- an atmospheric constituent is what we m a y spheres m a y gain but not lose argon. L e t us call ingassing f r o m the a t m o s p h e r e into the reexamine the p r o b l e m from the perspec- b o d y o f the planet. In general, relative notive that there are p r o c e s s e s in which plane- ble gas a b u n d a n c e s in terrestrial planet attary a t m o s p h e r e s can lose mass. m o s p h e r e s are similar to those o f planetary First consider the role o f outgassing, for gases trapped in meteorites, but there are which the radioactive d e c a y product 4°Ar some significant differences, particularly for the ratio 36Ar/132Xe. F o r Venus, only a lower limit is available; the ratio e x c e e d s This paper is based on a talk given at the Conference 3000. F o r Earth, the ratio is 1300. H o w on Planetary Volatiles, Alexandria, Minnesota, October 1982. It has been supported in part by National ever, for Mars the ratio is only 280, which is Aeronautics and Space Administration Grant NGR 22- almost in the range of the meteorites o f 007-269. 100-200. 195 0019-1035/83 $3.00 INTRODUCTION

Copyright © 1983 by Academic Press, Inc. All rights of reproduction in any form reserved.

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It is known that xenon forms weak bonds with some minerals and that xenon is absorbed within the Earth to a greater extent than is the case for the other noble gases. Hence the above figure for the 36Ar/132Xe ratio must be considered a lower limit for the Earth. Later in this paper it will be argued that the ratio for the Earth is much higher than this lower limit and that the Earth has retained much primordial (although isotopically fractionated) xenon but essentially none of the other primordial abundances of the noble gases. The above ratios tend to indicate that there is also a great deal of xenon trapped in the interior of Venus and Mars. For the moment, the degree to which this interior xenon has been ingassed rather than initially accumulated into the interior must be a matter for speculation, but apparently the required amounts of xenon do not exist in terrestrial shales (Podosek et al., 1983). In this paper we consider, somewhat qualitatively, two catastrophic processes of atmospheric loss: atmospheric cratering and major planetary collisions. The latter is discussed in connection with the origin of the Earth's Moon. Such a major collision has a profound effect on the formation of a planetary atmosphere, and some aspects of this are discussed in the final part of the paper. ATMOSPHERIC EROSION

By atmospheric cratering or atmospheric erosion we shall mean the loss of atmosphere resulting from collisions of planetesimals with the atmosphere. This is a subject for which no quantitative data exist and for which there are no quantitative theories. Hence we may only proceed with a qualitative discussion. At the low end of the mass range, it is known that very small particles of interplanetary origin may be recovered from the upper atmosphere. It is evident that these particles heated a narrow column of air upon entry, but the heated air must have rapidly shared its heat with its surround-

ings, and none of the impacted atmosphere will have been lost. From this we may conclude that planetesimals with dimensions small compared to an atmospheric scale height are ineffective in the process of atmospheric erosion. Consider next a collision with a planetesimal having dimensions comparable to the atmospheric scale height. Even for an atmosphere like that of Venus the density of gas in the lowest scale height is small compared to the density of the planetesimal. Hence the incoming planetesimal suffers no significant retardation in its highly supersonic motion; the gas which stands in its way must be thrust aside with the generation of a strong shock in the gas. Such a shock is weakened by geometric dilution in the horizontal direction, but the component of the shock which propagates in the vertical direction undergoes acceleration and strengthening as is characteristic of any shock travelling down a density gradient. After traversing some unknown number of scale heights, the vertical shock velocity should exceed escape velocity, and hence the amount of atmosphere ejected will correspond to the volume of the incoming projectile in one of the upper scale heights of the atmosphere. It may be useful to make some comparison between these atmospheric cratering collisions and head-on collisions between stars, for which two-dimensional hydrodynamic calculations were carried out by Seidl and Cameron (1972). In these calculations a moderate amount of sideward acceleration is seen and results in a small amount of mass ejection, but most of the energy of the collision goes into shocks which propagate along the collision axis of the two bodies. As the energy of the collision is increased, there is relatively little effect on the sideward acceleration, with the main effect being the strengthening of the shocks along the collision axis. This means that the shock which propagates into the projectile upon collision with the ground, after traversing the incoming body, may contribute

ORIGIN OF TERRESTRIAL ATMOSPHERES to the vertical component of the shock generated in the surrounding atmosphere (although the density discontinuity at the interface will probably make this effect rather inefficient). For collisions with planetesimals having larger dimensions, the process will be relatively less efficient, but I would guess that the amount of material ejected would scale with the square of the radius of the incoming projectile, assuming that the projected area of the projectile is the important quantity. As the velocity of the incoming projectile increases, the amount of atmospheric ejection will be moderately increased, but much less than in proportion to the incoming energy. It is important that these atmospheric cratering processes be studied by numerical hydrodynamic calculations, which must necessarily be two dimensional. The astrophysical techniques needed for such studies have been developed. For any discussion of the effects of planetary cratering on the atmospheres of the terrestrial planets we must consider the values of the planetary escape and orbital velocities. For Venus, Earth, and Mars, the escape velocities are 10.3, 11.2, and 5.0 km/ sec, and the orbital velocities are 35.05, 29.80, and 24.14 km/sec, respectively. Because the values for the Earth and Venus are so similar, the relative efficiencies for planetary mass ejection by large planetesimals should be similar at the present time. But because the density of the Venus atmosphere at the base is greater than for the Earth, the amount of gas ejected in a collision would be greater. On the other hand, because of the higher temperature, the atmospheric scale height is greater, so that a projectile comparable in dimension to the Venus scale height would eject material more efficiently than the same projectile would on Earth. However, there are fewer such projectiles than those comparable in dimensions with the scale height in the Earth's atmosphere, and these latter projectiles would have a reduced efficiency in

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ejecting gas from Venus. If we wish to apply these principles to the case of the Mars atmosphere, several striking differences are immediately apparent. The much smaller mass of Mars (and correspondingly smaller escape velocity) lead to a larger atmospheric scale height, only partly offset by the lower atmospheric temperatures. Thus it is clear that from a size point of view, larger planetesimals are more efficient in ejecting Mars atmosphere than Venus or Earth atmosphere. Furthermore, because the orbital velocity of Mars is not very much less that those of the other two planets, and because random perturbations of the orbits of planetesimals will tend to give them velocities proportional to the orbital velocity of the planet whose orbit they are crossing, it is apparent that the ratio of projectile velocity to planetary escape velocity will be much higher on Mars. Therefore the general efficiency of atmospheric cratering should be higher for Mars than for the other planets. There is also an important temporal difference in atmospheric cratering for Mars. Venus and the Earth appear to have swept up their early orbital-crossing planetesimals rather quickly when the planets were no doubt considerably hotter than now, whereas in the case of Mars this sweepingup process seems to have extended o v e r l 0 9 years or more, as was first pointed out by Opik (1951), at which time Mars would be relatively cool. On the one hand, this extends the major atmospheric cratering process into the era when much of the 4°Ar outgassing would take place, thus letting this atmospheric constituent participate in the erosion process whereas it would not have done so for the most part on Venus. Thus part of the apparent lack of outgassing of 4°Ar from the Martian interior may be attributable instead to atmospheric erosion. It is not possible from the lack of quantitative understanding of these processes to make meaningful estimates of the total amounts of atmospheric erosion from Venus and Mars that has taken place. I believe

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that it may have been quite substantial. The terrestrial planet atmospheres are clearly of secondary origin because of the resemblance of the ratios of the noble gas abundances to the planetary gas components of meteorites. This means that the noble gas contents of these atmospheres were brought into the planets by the same planetesimals whose collisions we are considering. A planetesimal with dimensions comparable to an atmospheric scale height is likely to eject more of the noble gas content of the atmosphere than it replenishes. However, that is the most efficient case. While a decent quantitative estimate for the whole process cannot be made, atmospheric erosion must be considered a major process in the formation of a planetary atmosphere.

ORIGINS OF THE MOON AND THE TERRESTRIAL ATMOSPHERE

We now turn our attention to major collisions between bodies of comparable size, and use as an example the major collision that may have been responsible for the formation of the Earth's Moon. The more dynamical aspects of this problem have previously been discussed by Cameron and Ward (1976) and Ward and Cameron (1978). Our original motivation for considering this problem came from asking how large a projectile would be needed to give the protoearth an angular momentum equal to that now possessed by the Earth-Moon system. Although it will turn out that the problem should really be done in the center of mass system, we are interested only in the order of magnitude of the result and hence will assume that the projectile is much smaller than the protoearth. Consider the protoearth to have mass ml and radius R and to be struck by a projectile of mass mz ~ m~ at a projected radial distance r, the projectile having velocity v2 at infinity and WEat collision. Energy conservation requires mErE2~2 = mEw22/2 -- G m l m E / R .

If the angular momentum at collision is

the present value for the Earth-Moon system, then m2w2r = 3.5 × I041 gm cm2/sec.

The mass of the postulated projectile is minimized for a glancing blow, so we take r = R. Then m 2 ~ 5 X 1026

gm

for a range of v2 up to a few kilometers/ second. This is nearly the mass of Mars. If we make the assumption that planetary-size bodies formed quite quickly in the primitive solar nebula, then both the protoearth and the projectile would be differentiated at the time of the impact. If the initial formation stage for such bodies involves nebular instabilities and the formation of giant gaseous protoplanets, followed by sedimentation of solids and thermal evaporation of gaseous envelopes, as I believe to be likely (Cameron, et al., 1982), then the number of giant gaseous protoplanets should exceed the present number of planets, since each axisymmetric (ringlike) instability in the gas should produce a few giant gaseous protoplanets. Many of these will collide immediately, but some will be perturbed into orbits of considerable eccentricity, and hence will collide with other terrestrial planets in a typical time of the order of 10s years or so (Opik, 1951). However, even if the terrestrial planets accreted entirely by Safronov-type collisions among solid bodies, it is reasonable to expect in a given region of accumulation that the second most massive body may have about 10% of the mass of the largest body (Wetherill, 1980). Typical rocks are vaporized at impact velocities of 9 km/sec or greater (Ahrens and O'Keefe, 1972). The impact velocity for the collision under consideration would be at least 11 km/sec and perhaps a few kilometers/second greater. If planetary mantles in the colliding bodies are liquid, vaporization would be even more extensive at these velocities. Thus it appears that significant portions of the mantles (but not the cores) of

ORIGIN OF TERRESTRIAL ATMOSPHERES both the protoearth and the projectile would be vaporized in the collision. Consider what would happen to such vapor. The vapor can expand only by a moderate factor before recondensation takes place. During the vapor phase the mass responds to gravity and pressure gradients, but after recondensation the matter just responds to gravity, although many collisions among small bodies may simulate the effects of a pressure gradient. All material ejected from the site of the collision travels on paths emerging from the surface of the protoearth. Purely ballistic trajectories would return such material to recollide with the protoearth as long as the orbits were elliptical. Material can be placed in orbit only if nongravitational forces cause deviations from ballistic paths. Pressure gradients operating on vaporized silicates are expected to play this role. The forward edge of the gas cloud will be accelerated into circumterrestrial orbit, but the yield of such orbiting material will be a relatively small part of the total colliding mass. Most of the mass in the forward edge of the gas cloud comes from the protoearth itself. The orbiting material consists of recondensed solids (probably about a centimeter in radius) which collide among themselves sufficiently rapidly to act much like a fluid. Safronov (1969) and Goldreich and Ward (1973) have discussed gravitational instabilities in a thin disk of particles. Ward and Cameron (1978) have discussed this instability for a circumterrestrial particle disk inside the Roche lobe. The instability takes place repeatedly, producing partial collapse of local regions in the disk which are then sheared apart. The process releases a great deal of energy by dissipation and spreads out the disk in the manner described by Lynden-Bell and Pringle (1974). The outwardly spreading part of the material collects to form the Moon beyond the Roche lobe. The estimated time scale given by Ward and Cameron was months to years, but Thompson and Stevenson (1983) have

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pointed out that for this time scale the dissipation would heat the disk to about 6000°K. Hence vaporization limits the rate of the process and maintains the temperature nearer to 2000°K out to the vicinity of the Roche lobe. Consider now the energy released in the collision of the projectile with the protoearth. For a simple illustration, consider merging two constant density spheres of 0.1 and 0.9 earth masses to form a new sphere of the same constant density p. The energy released is E = ~(4zrp/3)l/3GMS/3(1

-

0 . 9 5/3 -

0.15/3)

where M is the mass of the Earth. For p -5.517, energy release is 3 x 1038 erg. The real energy release would be about 10% greater because of central condensation in the model. This is 5 x 10 I° erg/gm which is more than ample to vaporize rocks at lower pressures. In an unpublished thesis, J. A. Teller (1973) calculated models of very hot Earths with iron cores and magnesium silicate mantles. The models were convective through an atmosphere of silicate decomposition products to a limit at a cloud layer of condensed silicate particles. The coolest of his models has a central temperature of 6000°K, a surface (cloud) temperature of 1165°K, and a thermal energy of 3.76 x 1038 erg. This is approximately the thermal energy released in the collision. If the bodies were very hot before the collision, then Teller's 8000°K central temperature model is of interest. It has about the same surface temperature and a thermal energy content of 5.19 x 10 38 erg. With a real gas atmosphere the silicate cloud temperature would be much higher. The Moon which is formed in this way will have extremely low abundances of the more volatile elements. These stay in the vapor phase and are likely to be lost from the disk together with the primordial atmosphere. The Moon will also be very poor in metallic iron. It is expected that the iron will have gathered in the cores of the pro-

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toearth and the projectile by the time of the collision, and it will not be vaporized in the collision. Those siderophile elements which would be carried into the cores by the iron will also be low in abundance in the Moon. The Moon should be formed close to the plane in which the collision takes place. The angular momentum of the protoearth before collision will add to that imparted by the collision. Hence it is unlikely that the silicate disk will lie precisely in the equatorial plane of the postcollision Earth. The following postcollisional picture emerges. In the vicinity of the protoearth and extending out to the Roche lobe (2.8 Earth radii) in or near the equatorial plane the temperature will be in the vicinity of 2000°K. At the Roche lobe the escape velocity is 6.7 km/sec and circular orbital velocity contributes 4.7 km/sec. Hence a gas atom needs 2.0 km/sec to escape in the minimum energy direction. Under these conditions the mean velocity of xenon atoms is about 40% of the minimum energy escape velocity. These conditions last for perhaps a century or so. We have seen that the postcollisional protoearth has a very high surface temperature and hence a large lower atmospheric scale height. Hence the atmosphere will interact with the silicate disk, and, since the silicate disk is self-gravitating, friction with the disk will spread the atmospheric gases along the surfaces of the disk and the gases will reach the Roche lobe when the disk does. This is sufficient for essentially all of the lighter noble gases and most of the xenon to escape. In fact, there is probably a hydrodynamic flow established in which heavier atoms will settle out as in the lower corona of the sun. Consider the implications of this picture for the primordial atmosphere of the Earth. Since Venus and the Earth have about the same mass, the simple expectation would be that the primordial Earth atmosphere would have about the present mass of the Venus atmosphere, or about 72 times the present Earth atmospheric mass, based on 36At. Actually this is a lower limit.

According to R. O. Pepin and D. Phinney (unpublished preprint) the fractionation of light xenon isotopes indicates that the present xenon in the Earth's atmosphere is 10-2 to 10-3 of that originally present. This xenon is the fractionated remainder of the xenon in the original primordial atmosphere of the protoearth and new unfractionated xenon added to the atmosphere since the time of the collision. The dominance of the fractionation pattern indicates that the fractionated remainder of the original xenon must considerably exceed (by a factor of about 4?) the abundance of the new unfractionated xenon added to Earth's atmosphere. This suggests that the primordial Earth atmosphere was at least several hundred times the mass of the present atmosphere. To finish on a speculative note, I would apply the above discussion to the interpretation of the large differences in the primordial argon abundances in the terrestrial planet atmospheres in the following way. The Venus atmosphere has probably been diminished by atmospheric erosion, but it comes closest to having preserved the incoming content of the noble gases. The Earth atmosphere lost essentially all its primordial argon at one point due to the Moon-forming event, and the amount present now represents that brought in by late accretion. Mars has lost the majority of its atmosphere by erosion. REFERENCES AHRENS, T. J., AND J. D. O'KEEFE (1972). Shock

melting and vaporizationof lunar rocks and minerals. The Moon 4, 214-249. CAMERON, A. G. W., W. M. DECAMPLI, AND P. BO-

DENHEIMER(1982). Evolutionof giant gaseous protoplanets embedded in the primitive solar nebula. Icarus 49, 298-312. CAMERON, A. G. W., AND W. R. WARD (1976). The origin of the Moon.Lunar Sci. VII, 120-122, Lunar Science Institute, Houston. GOLDREICH, P., AND W. R. WARD (1973). The formation of planetesimals.Astrophys. J. 183, 1051-1061. LYNDEN-BELL, D., AND J. E. PmNOLE (1974). The

evolutionof viscousdiscs and the originof the nebulax variables. Mon. Not. Roy. Astron. Soc. 168, 603-637.

ORIGIN OF TERRESTRIAL ATMOSPHERES MCELROY, M. B., AND M. J. PRATHER (1981). Noble gases in the terrestrial planets. Nature 293, 535-539. Opik, E. J. (1951). Collision probabilities with the planets and the distribution of interplanetary matter. Proc. Roy. It. Acad. Sect. A 54, 165-169. PODOSEK, F. A., T. J. BERNATOWICZ, M. HONDA, AND F. E. KRAMER(1983). The sedimentary inventory of atmospheric xenon. In Conference on Planetary Volatiles, pp. 139-140, LPI Technical Report 83-01, Lunar Planetary Institute, Houston. POLLACK, J. B,, AND D. C. BLACK (1979). Implications of the gas compositional measurements of Pioneer Venus for the origin of planetary atmospheres. Science 205, 56-59. POLLACK, J. B., AND D. C. BLACK(1982). Noble gases in planetary atmospheres: Implications for the origin and evolution of atmospheres. Icarus 51, 169-198. SAFRONOV, V. S. (1969). Evolution of the Protoplanetary Cloud and Formation of the Earth and Planets,

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Nauka, Moscow; transl., Israel Program for Scientific Translations, 1972. SEIDL, F. G. P., AND A. G. W. CAMERON (1972). A numerical hydrodynamic study of coalescence in head-on collisions of identical stars. Astrophys. Space Sci. 15, 44-128. TELLER, J. A. (1973). Unpublished thesis (Yeshiva University). THOMPSON, A. C., AND D. J. STEVENSON (1983). Two-phase gravitational instabilities in thin disks with application to the origin of the Moon. Lunar Planet. Sci. XIV, 787-788. WARD, W. R., AND A. G. W. CAMERON(1978). Disc evolution within the Roche limit. Lunar Planet. Sci. IX, 1205-1207. WETHERILL, G. W. (1980). Formation of the terrestrial planets. Ann. Rev. Astron. Astrophys. 18, 77-113. Wetherill, G. W. (1981). Solar wind origin of 36At on Venus. Icarus 46, 70-80.