III.C Long-term Evolution of the Zodiacal Cloud

The history of the zodiacal dust cloud over the age of the solar system is likely to have been closely connected to the history of the main asteroid belt. It is safe to state that the total mass of the asteroid population has steadily decreased and will continue to decrease due to mutual collisions and planetary perturbations. A "bulge" in the asteroid size distribution (Zellner 1979) provides evidence that the original population of the asteroid belt had a size spectrum concentrated between 50-100 km radius. Many if not all of the presently abundant asteroids smaller than that size range are not primordial but are collision fragments.

The total main belt asteroid population now has a collisional evolution time scale (population e-fold time) of a few x 10¹⁰ yr. The fact that this is significantly longer than the age of the system means that the evolution of the population is not "controlled" by mutual interactions but by something external, i.e. the planets. Many calculations have shown that asteroids in secular resonance with Jupiter (in the Kirkwood gaps) will eventually be thrown into planet-crossing orbits, some to exit the solar system. The winnowing of the asteroid belt is not just by collisions but also by planetary perturbations, so it is "chaotic" and the density of the asteroid belt and associated zodiacal cloud cannot be easily derived for past epochs.

The present total mass of main belt asteroids is estimated to be 5 x 10^-4 M_earth. It is possible that the original asteroid belt mass was 1000 times larger than present, i.e. 0.5 M_earth. The zodiacal dust released collisionally by that population could have been as much as 106 denser than the present cloud because collision rates depend on the square of the number of colliding bodies. Thus, the zodiacal cloud might have been enormously brighter earlier in the history of the solar system without a large belt mass relative to the major planets. A simple implication of this is that planet searches should be directed toward older stellar systems to avoid high dust density.