How Collisional and Dynamical Evolution Shape the Main Belt Size Distribution

D. P. O'Brien (University of Arizona) and R. Greenberg (University of Arizona) 


The size distribution of main-belt asteroids is governed by two main 
processes--collisional evolution and dynamical removal from the main-belt.  
Collisional evolution is due to the destruction of asteroids by high-velocity 
collisions and the subsequent production of smaller fragments.  Dynamical 
removal is due to the interaction of gravitational perturbations from the 
planets (resonances) with non-conservative forces such as the Yarkovsky effect 
which can push bodies into these resonances. Bodies are driven out of the main 
belt and into NEA space by the resonances.  Both the strength vs. size scaling 
law which governs collisional evolution and the non-conservative forces which 
drive bodies into resonances are size-dependent.  Thus, the size distribution 
of asteroids which results from the combined effect of collisional evolution 
and dynamical elimination will deviate from a simple power-law.  

We have developed a numerical model to study the combined effect of collisional 
evolution and dynamical elimination on the main-belt and NEA populations.  Our 
model tracks the collisional evolution of the main belt, subject to a given 
strength vs. size scaling law for asteroids, while simultaneously removing 
bodies from the population subject to a given size-dependent removal rate.  
Bodies which are removed from the main belt enter the NEA population, which 
decays exponentially due to dynamical effects.  Both the removal rate and the 
strength vs. size law can be varied in our model, and are the most influential 
parameters governing the shape of the final population.

In order to develop a consistent model of asteroid collisional and dynamical 
evolution, several lines of evidence must be reconciled.  First, our model 
must reproduce the observed size distribution of large asteroids in the main 
belt.  Second, lifetimes of meter-sized bodies must be consistent with the 
cosmic ray exposure (CRE) ages of meteorites.  Third, the population of small 
bodies must be able to reproduce the cratering record on observed asteroids 
(Ida, Gaspra, Mathilde, and Eros).  Finally, the NEA population in our model 
must be consistent with the observed NEA population.

We have found that removal rates consistent with current dynamical models 
[1], combined with scaling laws consistent with current impact models [2], 
can result in good fits to the main belt size distribution and yield lifetimes 
for meter-sized bodies consistent with CRE ages of stony meteorites.  Fitting 
the observed NEA distribution, however, has proven to be difficult, and may 
require a more detailed model of NEA delivery.  We are currently refining our 
model and we will present our most recent results.


[1] D. Vokrouhlicky, Pers. Comm.
[2] W. Benz, E. Asphaug (1999) Icarus, 142.