III.B Fluctuations in the General Zodiacal Cloud Density

The following argument leads to a conclusion that the present state of our solar system zodiacal cloud is probably comparable to its "normal" state over the past ~ 10⁹ yr:

1. Most of the present dust in the terrestrial-temperature zone is asteroidal rather than cometary. This is supported by Galileo and Ulysses observations, characteristics of the Earth's resonant ring, and properties of particles caught in Earth orbit by the LDEF (Long Duration Exposure Facility).

2. Collisions of 10 km-radius bodies should occur in the main belt approximately every 10⁷ yr ("particle-in-a-box" approximation, assuming 10⁴ such objects spread uniformly between 2.0 and 3.5 AU). One such collision could completely recreate the present zodiacal cloud. An example of a model history of the zodiacal cloud density (actually, of one family of collision debris) showing a general decline punctuated by large transient increases is presented in Figure 2.

   Figure 2 Model evolution of the total cross-section area of dust and other objects in a debris family generated by collision of two large asteroids at t = 0. The declining trend represents steady removal of particles by PR drag. The transient increases result from later collisions of large fragments within the swarm.

   
   
   
   

3. The presence of 3 obvious asteroid collision debris families indicates that complete dispersal of one of these families occupies a time span very roughly 3 x the 10⁷-yr interval between their initiation, much longer than the 10⁶-yr time scale for clearing 10-100 µm grains from the main belt by PR drag. This is consistent with the expectation that dust from a major collision is released slowly via grinding of large co-orbiting fragments rather than immediately in the initial collision.

4. Although the 3 known collision families are directly responsible for about 10% of the general dust population, fragments from those families may be responsible indirectly for much more of the zodiacal cloud via erosion of other asteroids ("erosional cascade"). If that is actually the case, the general cloud density could be connected directly to the number and density of active collision debris families.

5. Zodiacal cloud enhancements by significant collisions last long enough to overlap in time so the overall normal state of the cloud is probably determined by the average of a number of collision families in various degrees of relaxation.

6. A crude estimate might then indicate that the normal variation about the present state would be 3 ± 3 major collision families active at a given time (with associated general belt asteroid erosion), i.e. variation by a factor of ~ 2.

7. Increases in the zodiacal cloud density by factors of 10 or more due to exceptionally large asteroid collisions, giant comets, or comet showers probably occupy only a small fraction of the total time.
   
   Thus, the tentative conclusion is that the present zodi cloud density and brightness is probably the normal state, within approximately a factor of 2, for the present asteroid and comet population.