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Marsden, B. G. 1968, Comets and Non-gravitational Forces. Astron. J. 73, 367-379.
KESSLER: I have always been leary of comparing observational data from two different sources. For example, the probability of observing a fireball of a given mass may vary as something like velocity to the third or fourth power, whereas the probability of observing an asteroid or comet in space may be inversely proportional to velocity. The results would be to reduce the relative number of high-velocity fireballs and perhaps increase the number of high-velocity asteroids or comets. I am wondering if you considered these selection effects; and, if so, what effects they would have on your conclusions. WETHERILL: There are only a few comets known with aphelia between 4.5 and 5 AU. However, whether there are more or less is minor in importance. Any of these will evolve in such a way as to give a similar distribution on the velocity-elongation diagram. Whether there are strong biases in the Prairie Network can best be answered by McCrosky. McCROSKY: The bias is in favor of observing higher velocity objects. WHIPPLE: I question the large radii obtained by Wood and Goldstein. How can one have very much confidence in the radiation loss on a body which we know so little about? The outer surfaces of asteroids could have very low thermal conductivity and prevent heat loss. Consequently the interior could have been much hotter and the bodies would have been considerably smaller. It is very hard to know what value to put in. ANDERS: Fricker considered a thin surface layer but it was not significant. If you make it thick enough it will be significant. ARRHENIUS: There is another way to approach this discrepancy; that is, by the rather large uncertainties in the cooling rates. The diffusion coefficients that are used are extrapolated from higher temperatures, and there are rather large uncertainties. Another one is based on the fact that minor components such as phosphorus and hydrogen will increase the diffusion rate. All this would work in the direction of making the size of the body smaller. WETHERILL: I would like to say something about this question of large bodies. I do not see any compelling reason for not believing that asteroidal and cometary masses are distributed in a similar way. Most of the asteroidal mass is in a few large bodies, and hence these few large bodies might be expected to contribute most asteroidal fragments. In the same way, most of the cometary fragments could be derived from a few large comets rather than a large number of small ones.
UREY: It seems to me that the rather large objects must have been present in the primitive solar nebula and that they collided with the planets during their accumulation. In this way the tilt of the axes of the planets from the vertical to the ecliptic plane can be accounted for; and, in fact, the reverse rotation of Venus and the tilt of the axes of Earth, Mars, Uranus, and others with the exception of Jupiter must have originated in this way. I have suggested that many lunar-sized objects were present. It has been discussed by Marcus, Safranov, and, more recently, by Singer. The particular case of Uranus was called to my attention by Gold quite some years ago.
KENKNIGHT (submitted after meeting): Although comets might be attractive for meteors and some chondrites, the chemistry of the achondrite meteorites strongly suggests origin on, or in association with, a large enough body to have been strongly heated at origin. The chemistry and mineralogy of achondrites suggest a magmatic relation to material of the chondrite type. The structure and composition of the brecciated achondrites suggest histories as complicated as lunar surface breccias, including magmatic differentiation, brecciation or surface effusion, recrystallization, and further brecciation (Duke and Silver, 1967). Wasson and Wai (1970) give 11 reasons for believing the enstatite chondrites and enstatite achondrites form a systematic sequence driven by a heat source external to the parent body that was increasing with time and sufficiently intense to cause partial melting of silicates. The occurrence of gas-rich achondrites and the specific pattern of enrichment in C, Ni, Br, and Bi in addition to the noble gases in these achondrites suggests (Mazor and Anders, 1967; Müller and Zahringer, 1966) that carbonaceous chondrite material was added as an impurity at a parent body surface and then incorporated in a breccia during impact. These conditions at or near a meteorite parent body surface are consistent with the identification of the surface reflectivity of Vesta in the earlier paper by Chapman, Johnson, and McCord' with a eucritic achondrite, Nuevo Laredo.
WETHERILL: KenKnight's statement covers a very wide amount of territory in a very few sentences, some of which I agree with, some of which I do not. Therefore, I will confine my remarks to his first sentence, which may be taken to represent a summary of the remainder. I agree that the chemistry of the achondritic meteorites strongly suggests origin in a large enough body to have been strongly heated at the time of its formation. The same is true of the metamorphosed chondrites for that matter. On the other hand, we do not know if asteroids were strongly heated at the time of their formation, nor do we know that the cores of the comets were not. We do know that this heating took place during the formation interval of the solar system; and, therefore, an understanding of the very complex processes that took place in this interval is necessary to discuss these questions in a meaningful way. I am not convinced that any of us know that much about it, even though some people purport to.
Duke, M. B., and Silver, L. T. 1967, Petrology of Eucrites, Howardites, and Mesosiderites. Geochim. Cosmochim. Acta 31, 1637-1665.
Mazor, E., and Anders, E. 1967, Primordial Gases in the Jodzie Howardite and the Origin of Gas-Rich Meteorites. Geochim. Cosmochim. Acta 31, 1441-1456.
Müller, O., and Zahringer, J. 1966, Chemische Unterschiede bei Uredelgashaltigen Steinmeteoriten. Earth Planet. Sci. Lett. 1, 25-29.
Wasson, J. T., and Wai, C. M. 1970, Composition of the Metal, Schreibersite, and Perryite of Enstatite Achondrites and the Origin of Enstatite Chondrites and Achondrites. Geochim. Cosmochim. Acta 34, 169-184.
IS WATER ICE THE MAJOR DIFFERENCE BETWEEN COMETS AND ASTEROIDS?
A. H. DELSEMME
The nature of the volatile phase in comets has never been established from observations. Although water was likely to be its major constituent, evidence was still circumstantial. It is shown here that water evaporation quantitatively explains not only the brightness of the hydrogen and hydroxyl halos observed by the OAO for the two bright comets of 1970, but also, which is much more convincing, it explains their brightness dependence on the heliocentric distance.
The existence of a volatile phase, whatever it is, seems to be, of course, the major chemical difference between a “normal” cometary nucleus and a standard asteroid. This idea was used by Whipple (1950) to build his icy-conglomerate model, which explained in a qualitative way the nature of the so-called nongravitational forces acting on comet Encke. However, the chemical nature of this icy phase has not yet been positively identified. Therefore, the nongravitational force theory, developed for many comets by Marsden (1968, 1969), suffers from having no physicochemical model able to describe, in particular, the dependence of the acting force on the heliocentric distance.
The only molecule of the icy phase that cannot be reasonably doubted is water. There are many circumstantial reasons that I will not try to review again here. They range from the type of chemical considerations that were so successfully introduced by Urey into the study of the solar system and its origin, up to the recent observations of the hydrogen and hydroxyl halos by the OAO for the two bright comets of 1970 (Blamont, 1970; Code, Houck, and Lillie, 1970), to which I have just learned that we should add comet Encke. Previously, I have shown (Delsemme, 1971) that water evaporation explains the right order of magnitude of the brightnesses of the two halos. The major uncertainty comes from our ignorance of the albedo (or of the radius) of the cometary nucleus concerned. The right order of magnitude is reached if the albedo is between 0.10 and 0.90. It is obvious that when the albedo is larger than that, the energy absorbed diminishes drastically and the ices do not vaporize enough any more.
This shows how such an argument heavily depends on the model adopted. The other arguments for water are of an even more circumstantial nature and could be turned around easily. For instance, OH and H could be described as free radicals from the nucleus, using the ideas independently proposed by Haser (1955) and by Donn and Urey (1956). In this case, Levin's (1943, 1948) ideas on desorption could still be used.
Of course, the large brightness of the two halos makes these ideas rather unlikely. On the other hand, OH and H could come from one or several other molecules more complex than water. This cannot be ruled out because we still do not know very much about either the early chemical history of the cometary nucleus or the hypothetical parent molecules of the other free radicals observed in the cometary heads.
A new quantitative argument for the presence of water can be developed from the observed brightness dependence on the heliocentric distance of the hydrogen and hydroxyl halos. It is based on Code's (1971) observations, in particular of comet 1969g. On the log brightness versus log heliocentric distance diagram, the eight observed points draw a perfectly straight line for OH. For the Lyman-o emission, seven of the nine observed points also draw a straight line. Two points that are lower than the straight line are explained by Code as a spurious effect that is clearly understood (telluric reabsorption of part of the halo light because of the geometry). The slope for both OH and H is exactly the same. Code mentions a dependence on distance to -5.8 power. In the preprint kindly communicated later by Dr. Code, I find a slope n = -5.9 + 0.1. Because it is almost exactly 6, I propose here that the emission of light by the hydrogen and hydroxyl halos is in each case a three-step process in which each step shows, at least in a first approximation, an inverse square law dependence. The three steps proposed are
(1) Vaporization of water snows from the cometary nucleus
The production rate of H2O vapor by the first process depends on the total energy flux absorbed by the cometary snows, which varies as the inverse square law if the temperature of the cometary snows does not vary. The correction introduced by the temperature dependence on the vaporization rate of the snows gives a slope that is not exactly 2, but remains a constant at heliocentric distances smaller than 1.3 AU. The slope is between -2.15 and -2.05 depending on the accepted values for the snow albedos in the visible and in the infrared (Delsemme and Miller, 1971). An average value of -2.1 therefore can be used. It remains true for all types of snow.
The photodissociation described in the second step depends, of course, on the photon flux, which also follows the inverse square law. This photodissociation can be obtained by absorption of the solar flux, either in the first or in the second continuum of water (McNesby and Okabe, 1964), giving reactions (1) or (2), respectively:
As the two continua overlap, the ratio of the rates of the two processes is not known with accuracy; but the first one must strongly predominate because there is much more energy available in the solar spectrum between 180 and 140 nm than between 140 and 115 nm.
For the third step, H and OH must be distinguished. H is produced in the ground state and must therefore absorb a solar photon again, introducing the third dependence on the inverse square law, before emitting Lyman-o. radiation.
The same third step is followed by the OH molecules produced by reaction (1) in the ground state. But if they were produced by reaction (2) in their excited state, they would bypass the third step and immediately radiate the molecular band A2X* → X2II.
Provided that the heliocentric distance of the comet does not vary too much during the time of flight of the molecules or atoms through the whole coma (which is almost always true) and provided that the optical depth effects do not vary too much during the range of distances covered, because the global brightness in Lyman-o light (or in OH light) is practically proportional to the production rate of the H atoms (or of the OH radicals) in their excited state, one has
where Z is the production rate of molecules by vaporization, f is the photon flux of the Sun, and r is the heliocentric distance. If H2O were dissociated by process (2) only, the exponent of r would still be 6.1 for H (Lyman o) but would be 4.1 for OH. The observation of the slope n = -5.9 + 0.1, both for H and OH, seems to point out that process (1) is overwhelming and, by the same token, confirms for the first time in a more quantitative way the likely presence of water ices or snows in comets and the three-step mechanism of production of OH and H. It seems very difficult to keep a three-step mechanism by using something other than water. Direct desorption of radicals would give a two-step process with n = 4 or less. Dissociation of larger molecules would give, by and large, at least one more step for either H or OH. When better observations are known, it is hoped that mechanisms of this type will explain the physical processes and the origin of the other radicals observed in cometary heads. On the other hand, the evaporation of water could be used with more confidence to provide a physical meaning in Marsden's formulation of the nongravitational force.