[231] 14.1. BASIC PROBLEMS

The properties of the comet-meteoroid population have been described in ch. 4. It was pointed out that the definite correlation between comets and meteor streams, as defined in sec. 4.6.2, showed that they must be genetically related. We have to consider, however, whether the meteoroids derive from comets, comets are accreted from meteor streams, or the processes are reciprocal. In fact, the basic questions to be answered are

(1) What is the physical nature of the cometary nucleus? (a) Does it invariably consist of one single monolith? Or (b) could it, in some instances, consist of a larger number of bodies and lack physical coherence?

(2) What is the genetic relationship between comets and the meteor streams with which they are associated? (a) Do the stream meteoroids invariably derive from the associated comets or (b) is the process the reverse one? Or (c) are both processes possible?

(3) Is there a net dispersion or accretion during the lifetime of a comet?

(4) What is the origin of short-period comets?

(5) What is the origin of long-period comets?

Several other questions with regard to the chemical composition of the nucleus, the mechanisms for the production of the observed radicals and ions, and the nature of the interaction between comets and solar wind are also of genetic importance.

14.2. POSITIVE AND NEGATIVE DIFFUSION; METEOR STREAMS AS JET STREAMS

The answers to all these questions are basically connected with the problem of how a swarm of particles in similar orbits will develop. There has long been a general belief that collisions (and other types of interaction) between such particles will result in dispersion. As we have seen in ch. 6, this is correct only under the assumption that the collisions are elastic (or have at least a minimum of elasticity). However, an assemblage of particles in periodic orbits whose collisions are sufficiently inelastic will behave in the contrary way; i.e., pass from a dispersed to a less dispersed state (sec. 6.6).

As we do not know the collisional properties of meteoroids in space, it is [232] impossible to decide whether the diffusion in a stream of particles is positive or negative. This cannot be clarified by the study of the present collisional properties of meteorites that have fallen down on the Earth because any loose surface material, which may control the collisional behavior of meteorite parent bodies, has been lost during the passage of the meteorites through the atmosphere.

Study of the composition and texture of meteorites (ch. 22) demonstrates, however, that most groups consist of grains that were originally free from each other or loosely attached and that the material became compacted and indurated in the course of their evolution, so that durable pieces could survive travel to Earth.

Luminosity and deceleration studies of stream meteoroids in the Earth's atmosphere lead to the conclusion that the majority of these have mean bulk densities under 1.0 g/cm³, independent of mass (Verniani, 1967, 1973). This suggests that they are fluffy and probably have low elasticities, as further discussed in Sec. 7.4.

The first alternative (positive diffusion) leads necessarily to the more generally accepted theory of the comet-meteor stream complex (Kresak, 1968) which supposes that stream meteoroids derive from a monolithic block of ice and dust (Whipple's "icy conglomerate") and must diffuse both along and normal to the stream to be ultimately dispersed into interplanetary space (sporadic meteors). Such a theory bypasses the question of identifying a physically acceptable mechanism by which the monolithic cometary nucleus would have formed initially.

According to the second alternative (negative diffusion), a meteor stream can be kept together or contract under the condition that the self-focusing effect exceeds the disruptive effects due to planetary perturbations and solar radiation (Poynting-Robertson effect, etc.). As shown by Mendis (1973) and by Ip and Mendis (1974), this seems likely to occur under very general conditions. Hence a meteor stream may behave as a typical jet stream discussed in ch. 6. Their analysis also shows that the strong focusing by inelastic collision may be preceded by a transient phase of expansion of the stream. Due to its very large accretion cross section, a meteor stream may also be able to collect a significant amount of interplanetary dust and gas (Mendis, 1973).

14.3. ACCRETIONAL MECHANISM IN METEOR STREAMS

As the density in present-day meteor streams is much smaller than that in the jet streams discussed in ch. 12, it is possible that the accretional mechanism is of a somewhat different type.

[233] Trulsen (1971) has shown that planetary perturbations of meteor streams, rather than producing a general disruption, may cause density waves that build up slowly. If a number of such waves are forming, very large density increases can be caused statistically at some points, leading to the formation of a dense cloud of particles. These particles would ultimately agglomerate into a number of large aggregates which may accrete to form one body. This view then leads not to a model with a singular state of the cometary nucleus (as Whipple's "icy conglomerate" or Lyttleton's "sand bank"), but rather to a hierarchy of states ranging from a dispersed cloud of small particles to a single nucleus, with the latter the most likely final stable state.

Therefore, although many comets possibly do have a single central nucleus, perhaps of the Whipple type, it seems likely that there are comets with more than one nucleus or consisting of a more or less loose swarm of bodies of varying size. Indeed, the very dusty, gas-deficient comets may belong to the latter type. There are several instances of observation of comets with multiple nuclei (Richter, 1963, p. 152; Lyttleton, 1953; Mrkos, 1972). Whether these are the remnants of a single nucleus or merely the precursors of one is an open question. The latter alternative is consistent with accretion theory which explains how bodies such as monolithic cometary nuclei, asteroids, satellites, and planets can form in the first place.

14.4. OBSERVATIONS OF COMET FORMATION IN A METEOR STREAM

The formation of comets in meteor streams is supported by a number of observations. The comet P, Temple-Tuttle (T33.2 yr) was first recorded as a diffuse but bright object as recently as 1866 (Lovell, 1954), although the associated Leonid meteor stream was known for centuries earlier. Comet P/Swift-Tuttle (T120 yr) was bright enough on its first apparition to be easily seen with the naked eye, being a second-magnitude object at its brightest (Vsekhesviatsky, 1958). Although this spectacular short-period comet appeared as such for the first time only as late as 1862, its associated meteor stream, the Perseids, has been observed for over 12 centuries (Lovell, 1954). Under these circumstances it seemed reasonable to contemporary scientists to question the assumption that meteor streams always form from comets and to consider the possibility that these new comets were forming from the ancient meteor streams (Nordenskiold, 1883, p. 155).

Several reputable observers in the past claimed to have actually witnessed the formation of cometary nuclei; see review in Lyttleton (1953). More recently, Mrkos (1972) reported that in the most recent apparition of P'Honda-Mrkos-Pajdusakova no nucleus was originally detectable although the comet came very close to Earth ( < 0.3 AU) and hence could be observed [234] in detail. As the comet progressed in its orbit away from the Earth, not just one center of light but several appeared. Mrkos states that similar behavior also has been observed in earlier apparitions of this comet, which is probably also associated with a meteor stream ( Capricornids).

14.5. LONG- AND SHORT-PERIOD COMETS

The origin of long-period comets will later be discussed in the same general context as the formation of planets (ch. 19); the long-period comets are thus assumed to derive from assemblages of planetesimals in similar orbits.

As for the origin of short-period comets, the commonly accepted view has been that they derive from long-period comets that pass near one of the massive planets (especially Jupiter) and lose energy in the process. While a single close approach to Jupiter by the observed distribution of long-period comets cannot produce the observed distribution of short-period comets (Newton, 1891; Everhart, 1969), Everhart (1972) has recently shown that such a distribution could be the cumulative result of many hundreds of passages near Jupiter by near-parabolic comets having low inclinations and initial perihelia near Jupiter's orbit.

It is, however, doubtful if Everhart's calculations can resolve the crucial problem with regard to the origin of short-period comets; namely, the large observed number of these objects. Joss (1972) has shown, on the basis of Oort's comet cloud and the injection rate of new comets from this cloud into the inner solar system, that the above calculations fail by several orders of magnitude to explain the observed number of short-period comets. Delsemme (1973), however, has shown that if one also takes into account the intermediate period distribution and looks at the number of comets reaching perihelion per unit time, this difficulty is mitigated. However, due to the large number of assumptions inherent in Delsemme's calculation, it is not entirely convincing that the difficulty has been completely removed. One can also get around this difficulty, but only at the expense of introducing a new ad hoc hypothesis; namely, the existence of another population of long-period comets besides the observed one. This population would be distributed in a disc close to the ecliptic with dimension 10⁴ AU and containing over 10⁹ objects (Whipple, 1964; Axford, 1973); further discussion of this type of assumption is given by Mendis (1973).

Comets, since they exist, must obviously have previously been forming by some accretional process despite competing disruptive processes. If we assume that the same processes are operating today, and hence that comets may accrete from dispersed particles in similar orbits (meteor streams), then the crucial difficulty with regard to the observed number of shortperiod comets is overcome as has been shown by Trulsen (1971) and Mendis

[235] (1973). Meteor streams, according to this view, do not necessarily only represent a sink for short-period comets as has been generally believed, but they could also form a source. It is possible that a steady state may be maintained with the average rate of formational focusing of particles into short-period comets equaling the average rate of dispersion of cometary material into meteor streams (Mendis, 1973).

14.6. INFERENCES ON THE NATURE OF COMETS FROM EMISSION CHARACTERISTICS

The assumption of ices as important bonding materials in cometary nuclei rests in almost all cases on indirect evidence, specifically the observation of atomic hydrogen (Lyman emission) and hydroxyl radical in a vast cloud surrounding the comet, in some cases accompanied by observation of H₂0⁺ or neutral water molecules. In addition, CH₃CN, HCN, and corresponding radicals and ions are common constituents of the cometary gas envelope. These observations can be rationalized by assuming (Delsemme, 1972; Mendis, 1973) that the cometary nuclei consist of loose agglomerates containing, in addition to silicates (observed by infrared spectrometry (Maas et al., 1970)) and also water ice with inclusions of volatile carbon and nitrogen compounds.

It has been suggested by Lal (1972b) that the Lyman a emission could be caused by solar wind hydrogen, thermalized on the particles in the dust cloud surrounding the comet. Experiments by Arrhenius and Andersen (1973) irradiating calcium aluminosilicate (anorthite) surfaces with protons in the 10-keV range resulted in a substantial (~10 percent) yield of hydroxyl ion and also hydroxyl ion complexes such as CaOH.

Observations on the lunar surface (Hapke et al., 1970; Epstein and Taylor, 1970, 1972) also demonstrate that such proton-assisted abstraction of oxygen (preferentially O¹⁶) from silicates is an active process in space, resulting in a flux of OH and related species. In cometary particle streams, new silicate surfaces would relatively frequently be exposed by fracture and fusion at grain collision. The production of hydroxyl radicals and ions would in this case not be rate-limited by surface saturation to the same extent as on the Moon (for lunar soil turnover rate, see Arrhenius et al. (1972)).

These observations, although not negating the possible occurrence of water ice in cometary nuclei, point also to refractory sources of the actually observed hydrogen and hydroxyl. Solar protons as well as the products of their reaction with silicate oxygen would interact with any solid carbon and nitrogen compounds characteristic of carbonaceous chondrites to yield volatile carbon and nitrogen radicals such as observed in comets. Phenomena such as "flares," "breakups," "high-velocity jets," and nongravitational [236] acceleration are all phenomena that fit well into a theory ascribing them to the evaporation of frozen volatiles. However, with different semantic labels the underlying observations would also seem to be interpretable as manifestations of the focusing and dispersion processes in the cometary region of the meteor stream, accompanied by solar wind interaction.

14.7. ANALOGIES BETWEEN COMETARY AND ASTEROIDAL STREAMS

The main-belt asteroid population does not interact very much with the comet-meteoroid population but some analogous phenomena seem to occur there. The reason for this is that in both cases the interaction of a large number of small bodies produce similar results.

Among the main-belt asteroids there are a number of asteoridal jet streams (sec. 4.3.3). Each jet stream contains a number of visual asteroids which have almost the same values of semimajor axis a, inclination i, eccentricity e, and longitudes of the pericenter and node, and , and hence move in approximately similar orbits. Figure 4.3.6 is a profile of such a jet stream showing an example of dense distribution of orbits in space, which means that relative velocities between the bodies are small.

Each one of the large number of asteroidal families is characterized by their similarity in a, e, and i, but, in contrast to a jet stream, and , differ. Hence the orbits of the bodies in a family do not keep together but are spread out in space. If the bodies in a jet stream move according to celestial mechanics, unperturbed by interaction between the bodies, the secular perturbations from the planets will cause the orbits to precess at a rate that is a function of the orbital parameters, but a, i, and e will vary only within narrow limits. The spread of the parameters in a jet stream will produce random orientation of their and after a time of the order 10⁵- 1O⁶ yr. In analogy with the asteroidal jet streams and families, many meteor streams are well focused also in and , even though they may lack an observable comet, while others (more rarely) have and widely scattered.

The traditional view is that an asteroidal family is the product of an "exploded" asteroid or consists of the debris of a collision between two asteroids. From this point of view one would be inclined to regard a jet stream as an intermediate stage in this development of a family. The debris will first keep together, with the orbital parameters being similar for all orbits, and later be spread out with random and .

From a qualitative point of view such a development is quite reasonable. It is more doubtful whether it is acceptable quantitatively. A detailed analysis will be necessary before this can be decided. The profiles of a [237] number of jet streams must be analyzed and the number of jet streams must be reconciled with the length of time they can keep together.

For reasons we have discussed in sec. 7.3.3, accretion must be the dominant process in the asteroidal belt, and it seems reasonable to regard the asteroidal jet streams as products of the general jet-stream mechanism studied in ch. 6. This means that collisions between particles will perturb their motion in such a way that the orbits become more similar. However, this presumably cannot be done by interaction between the visual asteroids alone. There is obviously no reason to believe that the asteroids which have so far been observed are all that exist. To the contrary, the mass spectrum of asteroids is very likely to extend to subvisual asteroids, of which the majority will be very much smaller; how small is not known (see ch. 7) As, in practically all mass spectra of small bodies, the smallest bodies represent the largest cross section, the collisions between the subvisual asteroids will be much more frequent than those between the visual asteroids Hence the subvisual members of a jet stream will be most important for the exchange of momentum between the bodies in the stream. In other words it is the collisions between the subvisual asteroids which keep an asteroidal jet stream together.

Hence a reasonable sequence of evolutionary processes in the asteroidal belt would be the following.

A large number of small grains are focused together and form jet streams, which later accrete more grains. Within each stream, the relative velocities are gradually reduced so much by collisions that accretion of larger bodies begins, and, after some time, leads to formation of visual asteroids in the jet stream. As the process proceeds, the majority of the small grains are accreted by the largest bodies, so that eventually there is not enough collisional interaction to keep the jet stream focused. Planetary perturbation will then cause the members of the stream to precess with different velocities and a family with random and values is produced.

Throughout this development, there are high-velocity collisions between members of different jet streams and/or asteroids that are not members jet streams. Such collisions will produce debris that sooner or later will be incorporated in existing streams or form new jet streams. The net result may be a progressive concentration of mass into a decreasing number large bodies.

Evolution in the asteroidal belt is obviously a very complex process will various types of resonances complicating the situation still further, and what has been proposed here is only an attempt to present a reasonable sequence. Much theoretical work and much more observational data a needed before it is possible to decide to what extent these speculations a realistic.

[238] 14.8. COMPARISON WITH THE ACCRETION OF PLANETS AND SATELLITES

We have seen that, because of the low density in meteor streams, the mechanism of planetary and satellite accretion is not applicable. One may turn the question around and ask whether we need the accretional mechanism of ch. 12 at all. Perhaps the accretion of planets and satellites may also be due to density waves.

It seems likely that density waves may have been important, especially during the initial phase of accretion of planets and satellites. Thus it is possible that the application of the theory of cometary accretion will be a useful supplement to the theory for nongravitational accretion. It is less likely that the effects of density waves would have been significant in the runaway process and in the subsequent phase of accretion. Moreover, density waves are due to planetary perturbation and should be more easily produced in highly eccentric jet streams than in circular streams. On the other hand, the accretion of the outermost planets (delayed runaway accretion) implies jet streams of very low densities. It is possible that the cometary accretion mechanism may be more directly applicable in that case.

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