SP-345 Evolution of the Solar System

 

19. TRANSPLANETARY CONDENSATION

 

[325] 19.1. INTERPLANETARY AND TRANSPLANETARY CONDENSATION

In the preceding chapters we have studied planetary formation as the end product of two processes active in interplanetary space:

(1) Transfer of angular momentum from the Sun to a surrounding plasma.

(2) Condensation of the plasma.

There is necessarily a spatial limit to the first process because of the limitation of the distance to which the Sun can transfer angular momentum. There may also be an outer limit to the region in which condensation takes place, but it is unlikely that this coincides with the limit of momentum transfer. As we shall find, it is likely that condensation also took place far outside the transfer limit, giving a condensate with small angular momentum.

In this chapter we shall study this process, which we shall call transplanetary condensation since (by definition) it took place outside the region of the planets. The processes we discuss are basically the same as those we have studied earlier. Hence no new assumptions are necessary. The transplanetary condensation is essentially a corollary to our theory of planet formation.

As we shall find, the transplanetary condensation gives two important results:

(1) The formation of the comet-meteoroid population.

(2) The enrichment of condensable elements in the A, B, and C clouds (ch. 21). This process may have been essential in determining the chemical composition of the planets (and satellites).

 

19.2. LIMIT BETWEEN INTERPLANETARY AND TRANSPLANETARY SPACE

The planets acquired their prograde orbital motion from hydromagnetic transfer of solar angular momentum (chs. 16-17). There must be an outer limit to this transfer because the solar magnetic field can dominate only [326] out to a point where it becomes equal to magnetic fields of other origin. Usually the field outside the solar system is referred to as the "galactic magnetic field." This is a misleading term because the galaxy has the linear dimension 1023 cm and we are concerned with a region that is 10-8 to 10-6 less than this. The conditions in this close neighborhood of our solar system are unlikely to be representative of the galaxy as a whole. We will call this region the transplanetary region. The field outside the region where the solar field dominates will be called the transplanetary field.

If the solar magnetic dipole moment is mathematical symbol
, the field at a distance rLm is mathematical equationDenoting the transplanetary field by BTp we find

 

mathematical equation
(19.2.1)

 

As mathematical symbol
and BTp are likely to vary with time, rLm will change. The maximum value rTp which rLm reaches during a period of plasma emplacement defines the outermost region to which the Sun has ever been able to transfer angular momentum. We define this as the limit between interplanetary space and transplanetary space. Assuming that Pluto is the outermost member of the solar system, this limit should, according to ch. 17, be related to the orbital distancemathematical symbol
of Pluto by

 

mathematical equation
(19.2.2)

 

19.3. CONDENSATION OF BODIES IN ALMOST-PARABOLIC ORBITS

As we have found, bodies with prograde orbits are formed in interplanetary space but a similar condensation in transplanetary space, and also anywhere outside rLm, gives rise to a population with small and randomly distributed angular momenta. Introducing this difference in angular momentum we can apply the interplanetary processes that we have analyzed in chs. 16-17 to transplanetary space:

(1) Grains condense from the plasma, especially in dense regions. (Moreover, this medium may have already contained appreciable amounts of interstellar dust at an early stage.) The condensates in this region can be identified with sporadic meteors in long-period orbits.

(2) The grains are focused into jet streams (ch. 6). Some of these may [327] be identified with the observed long-period meteor streams, but most of them are difficult to observe.

(3) In these jet streams an accretion of larger bodies takes place (chs. 11 and 14). We identify these accreted bodies with long-period comets.

The concept of transplanetary condensation has been criticized on the premise that the plasma density far from the Sun is likely to have been very small and hence the time of condensation of a small grain would have been extremely large. This objection was based on the concept of a homogeneous model and was invalidated when it became apparent that space plasmas usually are inhomogeneous. In fact, even if there might be objections to a high average density, the density is likely to have been orders of magnitude larger locally. (See ch. 15.) Condensation of grains can take place in such high-density regions. Further, the grains may be focused into jet streams by the mechanisms discussed in ch. 6.

Hence, although we are far from a detailed theory of transplanetary condensation there is no obvious objection to such an approach and, as we shall see, quite a few observed phenomena are indicating that such a condensation must have taken place.

However, even if these processes have the same general character for transplanetary condensation as for interplanetary condensation, they do differ in certain aspects. We can understand fairly well that grains which condensed from a partially corotating plasma in interplanetary space are focused into jet streams. It is not so obvious that in transplanetary space grains in randomly distributed orbits will evolve into randomly distributed jet streams. This mechanism has to be investigated carefully. Further, formation of comets in a meteor stream does not necessarily proceed by the same mechanism as the formation of planets and satellites. The Trulsen (1972a) mechanism, involving a number of superimposed density waves, is probably more important.

 

19.4. BODIES WITH LONG-PERIOD ORBITS

As we have seen in ch. 4, the comet-meteoroid complex consists of two populations: the short-period population and the long-period population. Of the latter we know only those bodies which have their perihelia close to the Sun (less than 1 AU for meteoroids, less than a few AU for comets). These move in almost parabolic orbits with aphelia far out from the Sun. Typical orbits are given in table 19.4.1.

A body with aphelion at 20 000 AU spends about 1 million yr very far from the Sun in what Oort (1963) has called the cometary reservoir. It then makes a quick visit to the solar environment, spending about 80 yr inside the orbit of Pluto and about 4 yr inside the orbit of Jupiter. After....

 


[
328] TABLE 19.4.1. Long-Period Orbits.

Aphelion

Semimajor axis

Period

.

200 AU = 3 X 1015 cm

100 AU

1000 yr

20 000 AU = 3 X 1017 cm

10 000 AU

1 000 000 yr


 

....this rapid excursion, it returns to a million-year rest in the reservoir. For a body with aphelion at 200 AU the period of time in interplanetary space is essentially the same. If a slight correction is made for selection effects, the orbits of the long-period bodies are found to be completely random (Porter, 1963), from which one concludes that the cometary reservoir is at rest in relation to the Sun. It is not completely clarified whether this conclusion is based on a selection effect, due to the fact that only those bodies which have their perihelia close to the Sun can be observed.

Oort (1963) has suggested that the long-period comets were produced in the inner regions of the planetary system and ejected by Jupiter. Detailed orbital evolution calculations (Everhart, 1974) show that this mechanism is impossible. This result is also fatal to Whipple's theory (1972) of an origin in the Uranus-Neptune region. One is forced to conclude that the comets were formed by some process in the transplanetary region.

 

19.5. DIFFUSION OF ALMOST-PARABOLIC ORBITS: ENCOUNTERS WITH PLANETS

A body in an almost-parabolic orbit with perihelion inside Jupiter's orbit and aphelion far outside the orbit of Jupiter has a chance of 3 X 10-8 of colliding with Jupiter for every turn into the central region of the solar system. The chance for an approach close enough to cause a noticeable change in orbit (diffusion of aphelion) is given by Opik as 0.5 X 10-3 (Opik, 1963).

Consider a body with an orbital period TK yr, which was generated in the hetegonic era. If TK > 2 X 106 yr it will have made less than 2 X 103 visits to the central parts of the solar system, and it is not very likely to have been seriously perturbed by Jupiter. Hence, most of the very long-period population will still be in approximately the primeval state. This is consistent with the randomly distributed orbits of long-period meteoroids and comets. However, stellar perturbations of the cometary reservoir may invalidate this conclusion.

With decreasing TK there is an increase in the chance that a close approach to Jupiter (or some other planet) has taken place during the lifetime of the body. This leads to a diffusion which becomes more rapid the smaller [329] the orbital period. For an order-of-magnitude approximation we can put the diffusion time equal to 2 X 103 TK (see above). Hence the aphelia of orbits inside 1016 cm, corresponding to Kepler periods of some hundred years, will diffuse with a time scale of the order of less than a million years.

For bodies with perihelia outside the region of the terrestrial planets, the main risk of destruction is collision with Jupiter. For orbits with perihelia closer to the Sun, Venus and Earth provide another main collision risk with probability for a hit of the order of 3 X 10-8 per turn. As bodies in near-parabolic orbits with apherlia in interplanetary space have periods less than 100 yr, this means that most bodies which condensed in interplanetary space (but outside the temporary position of rLm) in the hetegonic era have been destroyed, unless they have diffused into orbits of longer periods.

 

19.6. GENETIC RELATIONS OF THE COMET-METEOROID COMPLEX

What we have found suggests a family history of comets and meteoroids as shown in fig. 19.8.2. The primeval transplanetary condensation produced the long-period meteoroids, of which many have been focused into jet streams (long-period meteor streams). Accretion inside these, probably due to density waves, produces the long-period comets. All these bodies move in almost-parabolic orbits with random distribution.

Planetary encounters of long-period meteoroids perturb their orbits into short-period, predominantly prograde orbits with lower eccentricities. These meteoroids are focused into short-period meteor streams, and short-period comets then accrete within these streams. The ultimate fate of the largest of these comets may be Apollo-Amor-type bodies ("burned-out comets"), which eventually collide with a planet.

In principle short-period comets could also derive from long-period comets which are "captured" by Jupiter. This is the same process that has produced short-period meteoroids from long-period meteoroids. However, the probability of this process is too small by several orders of magnitude to be of any importance.

In fact, the transition probability between almost-parabolic and captured orbits is of the order 10-6. (This should not be confused with the probability for a diffusion of the aphelion of a long-period orbit due to scattering by Jupiter.) As the period of Jupiter-crossing captured bodies is 10-100 yr, this means that a diffusion between different orbits takes place in 107-108 yr. This is lower than the mean life of a body like a meteoroid in interplanetary space, which is of the order of 108 yr, with the result that the population of the different orbits will be roughly equal.

[330] In striking contrast to the long lifetime of short-period meteoroids is the short lifetime of short-period comets, which according to observations is only 100-10 000 yr. This means that a diffusional equilibrium between long-period and short-period comets cannot be established. In other words, Jupiter is inefficient as a scatterer of long-period comets into short-period orbits. If the short-period comets were exclusively due to capture of longperiod comets their number would be three or four orders of magnitude less than observed.

This constitutes a serious inadequacy in the capture theory for shortperiod comets (Mendis, 1973). This difficulty can be circumvented by the ad hoc assumption of a special cometary reservoir close outside Jupiter, but there is no independent evidence for this. Further, an intrinsic difficulty of this theory is that it takes for granted the existence of long-period comets. Its only ambition is to refer the origin of short-period comets one step backward.

Within the approach used here, the short-period comets are considered to accrete from short-period meteor streams by the same process that produces the long-period comets as accretions in the long-period meteor streams. In this approach both types of objects follow a pattern of evolution which basically is the same as that of planets and satellites.

 

19.7. CONCLUSIONS ABOUT THE METEOROID POPULATIONS

In view of the fact that the time constant for collision of short-period bodies with planets is short compared to the age of the solar system, most of these bodies in interplanetary space must either have condensed there long after the formation of the solar system or diffused into this region at a later time. The first alternative is not attractive, because no independent argument seems to exist for such a late condensation. The second alternative is quite acceptable because the time for orbit diffusion is rather short, as found in sec. 19.5. In fact, as the time constant for orbit diffusion is much shorter than the time constant for collisional destruction, we may expect the meteoroid orbits to be in diffusional equilibrium, a result which may be checked observationally.

This means that the short-period meteoroids may very well originate from long-period meteoroids, perturbed ("captured") by Jupiter. As we have seen, the capture theory of short-period comets is not acceptable because quantitatively it is in error by a factor of 104. However, the same theory can be directly applied to meteoroids, where it probably works very well.

[331] Hence the theory of Jupiter capture of long-period bodies into shortperiod orbits is applicable to meteoroids, but not to comets. The reason for this is that the lifetime of meteoroids in interplanetary space is of the order of millions of years (i.e., long compared to the diffusion time), whereas the lifetime of short-period comets is known to be short, in the range 100 to 10 000 yr, which is short compared to the diffusion time constant for transition between long-period and short-period orbits.

What we have found suggests a genealogy of meteoroids and comets as outlined in sec. 19.8.2 and fig. 19.8.2.

 

19.8. GENEALOGY OF THE BODIES IN THE SOLAR SYSTEM

19.8.1. Traditional Approach

Figure 19.8.1 shows the traditional view of the genetic relationships between the bodies in the solar system. The asteroids are assumed to be debris of one or more exploded planets, which, like other planets, derive from a Laplacian solar nebula.

 


FIGURE 19.8.1.- Traditional view of genetic relationships between different types of bodies in the solar system.

FIGURE 19.8.1.- Traditional view of genetic relationships between different types of bodies in the solar system.

 

[332] The elliptic population, consisting of short-period comets and meteoroids, is supposed to derive from Jovian capture and deflection of long-period comets into short-period orbits. These comets disintegrate, giving rise to part of the short-period meteoroid population and, after scattering, a portion of sporadic meteoroids.

Long-period comets produce long-period meteoroids and sporadic meteoroids by a similar process. The origin of the long-period comets is accepted as unknown or is accounted for by hypotheses which are not integrated in a general hetegonic framework (see, e.g., Oort, 1963; Whipple, 1972; Cameron, 1973).

 

19.8.2. Present Analysis

Figure 19.8.2 and table 19.8.1 present the genealogy which results from the present analysis. The primeval condensation providing the source material for all the bodies takes place in both interplanetary and transplanetary space. (Some of the transplanetary material may derive from condensation at large distances in space and time.)

 


FIGURE 19.8.2- Genetic relationships between the different types of bodies in the solar system.

FIGURE 19.8.2- Genetic relationships between the different types of bodies in the solar system. This genealogy is based on the present analysis.

 


[
333] TABLE 19. 8.1. Orbital Populations in the Solar System.

ALMOST CIRCULAR e <1/3

.

ELLIPTIC 1/3 < e <0.95

.

ALMOST PARABOLIC e > 0.95

.

Summary

.

 

Summary

.

 

Summary

.

.

.

Originate from primeval interplanetary condensates augmented from the transplanetary reservoir. The angular momentum transfer process and viscous dissipation ultimately result in almost circular orbits of planets, asteroids, and satellites.

Because of collision with planets the lifetime is short and no primeval condensate remains today. The origin of elliptic orbits is diffusion by planetary perturbation of long-period meteoroids into short-period orbits.

Originate from primeval condensation in transplanetary space, beyond the influence of the solar magnetic field. Angular momentum is small.

 

.

.

.

Planets and satellites

Short-period meteoroids

Long-period meteoroids

.

.

.

Infinite lifetime and no orbital evolution

Arise mainly from scattered long-period meteoroids; asteroid debris can, in principle, contribute, but the transition probability is small.

Formed by accretion of condensates in the transplanetary reservoir. If the period is >5000 yr, planets do not perturb the orbit; if <5000 yr, meteoroids may be scattered into increasingly prograde short-period orbits.

.

.

.

Visual Asteroids

Short-period meteor streams

Long-period meteor streams

.

.

.

Slow evolution, on a time scale of 1011 yr, possibly toward formation of several planets.

Formed from short-period meteoroids.

Formed from long-period meteoroids.

.

.

.

Subvisual asteroids

Short-period comets

Long-period comets

.

.

.

Predominantly produced by accretion from small particles, but also from asteroid collisions. They interact mutually with other populations.

Accreted in short-period meteor streams. Long-period comets can, in principle, be captured by Jupiter into short-period orbits, but transition probability is very small.

Accreting in long-period meteor streams.

.

.

.

Microscopic particles

Apollo-Amor asteroids

Microscopic particles

.

.

.

Originate from asteroid and meteoroid collisions and cometary debris. Interact with all the populations.

Residue of short-period comets.

Originate from asteroid and meteoroid collisions and cometary debris. Interact with all the populations.

.

.

.

.

Microscopic particles

.

Originate from asteroid and meteoroid collisions and cometary debris. Interact with all the populations.


 

[334] The interplanetary condensation produces grains accreting to embryos (planetesimals) which, in turn, accrete to planets in the dense regions. In less dense regions the material is still in an embryonic stage of accretion, in the form of asteroids, visual and subvisual.

The transplanetary condensation primarily produces meteoroids in almost parabolic orbits. Some of these meteoroids will interact with the interplanetary condensates, contributing condensable components to this region. Long-period meteoroids can diffuse (by "Jupiter capture") into short-period orbits. Short-period meteoroids constitute the major component of the elliptic population. Both long-period and short-period meteoroids undergo the same evolution, forming meteor streams and eventually comets.

The micrometeoroids may have genetic relations with all the populations.


previouscontentsnext