The collisional evolution of really tiny asteroids: Implications for their 
size-distribution and lifetimes

David P. O'Brien and Richard Greenberg
Lunar and Planetary Laboratory, University of Arizona


The collisional evolution of small asteroids (tens of meters or less) in the 
main belt is constrained by several lines of evidence.  The cosmic ray exposure
(CRE) ages of meteorites give an estimate of the collisional lifetimes of 
meter-sized bodies in the asteroid belt.  Cratering records on the asteroids 
Ida and Gaspra can be used to constrain the size-distribution of small bodies 
in the main belt.  Finally, collisional evolution models of the main belt can 
be fit to the observed population of large asteroids and give an estimate of 
the size distribution and lifetimes of smaller bodies.
 
However, as pointed out by O'Brien and Greenberg [1], these lines of evidence 
are contradictory.  Durda et al. [2] found a strength vs. size scaling law 
which reproduced the population of observed asteroids (3 km and larger) when 
used in a collisional evolution model.  However, the scaling law and the 
population of small asteroids in the model resulted in lifetimes for meter-sized 
bodies of ~1 Myr (over an order of magnitude less than ordinary chondrite CRE 
ages).  Furthermore, the number of small bodies in the Durda et al. model is 
an order of magnitude lower than the population necessary to reproduce the 
cratering records on Ida and Gaspra [3,4]. 

We have improved the consistency between these different lines of evidence 
somewhat by tuning the scaling law, but there are still significant 
discrepancies.  Different scaling laws, including the hydrocode-derived 
scaling law of Benz and Asphaug [5], result in evolved populations which 
provide a reasonable fit to the cratering records of Ida and Gaspra and give 
lifetimes for meter-sized bodies which are on the order of 8 Myr (about half 
the CRE age of ordinary chondrites).  In adjusting the scaling law, however, 
the resulting population of large bodies is about a factor of 3 more numerous 
than the actual observed population.

Fully reconciling this inconsistency requires a more thorough exploration 
of the parameter space used in our collisional evolution model and our 
cratering record analysis, as well as the development of a more advanced 
collisional model. We have developed a collisional evolution model which 
takes into account the damping of the relative velocities of small bodies due 
to non-disruptive impacts and the removal of bodies due to Poynting-Robertson 
drag and the Yarkovsky effect, which have not been fully incorporated into 
asteroidal collisional evolution models before.  Both of these modifications 
result in perturbations to the evolving population which can affect the 
lifetimes of small bodies, change the slope of the model population, and 
affect the population of large bodies.  Results of our collisional evolution 
models thus have implications for reconciling the different lines of evidence 
for numbers and lifetimes of sub-decameter-sized asteroids. 


References: 

[1] O'Brien, D. P., and R. Greenberg 1999. Asteroids, Comets, and Meteors 
    Conference. 
[2] Durda, D. D., R. Greenberg, and R. Jedicke 1998. Icarus 135, 431-440. 
[3] Greenberg et al. 1994. Icarus 107, 84-97. [4] Greenberg et al. 1996. 
    Icarus 120, 106-118. [5] Benz, W. and E. Asphaug 1999. Icarus 142, 5-20.