The Main Belt and Nea Size Distributions: Linked Collisional and Dynamical Evolution

Overview: The size distribution of the main belt is governed by collisional evolution as well as by the non-collisional removal of bodies due to the combination of radiation forces and resonances. The NEA size distribution is governed in part by the size distribution of the main belt, it’s primary source, but differs somewhat from the main belt due to the size dependent processes which deliver asteroids from the main belt to near-Earth space. These two size distributions provide a powerful constraint on any model of asteroid collisional evolution and NEA delivery. Additional constraints are provided by the cratering records on observed asteroids, such as Gaspra, Ida, Mathilde, and Eros, and by the cosmic ray exposure (CRE) ages of meteorites, which indicate that meter-sized bodies have collisional lifetimes on the order of 10 Myr or more in the main belt. A collisional evolution model for the main belt can fit most of these constraints with reasonable parameter choices. In addition, our results show that non-collisional removal processes, such as the Yarkovsky effect, are not strong enough to significantly alter the cratering records on asteroids (i. e. incapable of causing a significant depletion in small craters, as seen on Eros). The Model: We use a numerical collisional evolution code based on the collisional algorithm of Petit and Farinella [1]. Our code starts with an initial binned main belt population and evolves this population through time. Collision frequencies are calculated using estimates of the intrinsic collision probability [2], and the Petit and Farinella algorithm is used to predict the outcomes of collisions between bodies in any two size bins. Both cratering and catastrophic collisions are treated. The main parameter we use that governs the collisional outcome is the critical specific energy , which is the energy per unit mass necessary to fragment a target and disperse half of the mass of the fragments to infinity. In addition to collisional effects, our code also treats the size-dependent removal of bodies from the main belt by noncollisional effects, such as the Yarkovsky effect, which sweeps main belt bodies into resonances that deliver them to near-Earth space. The bodies removed from the main belt population in our model become NEAs with a dynamical lifetime on the order of a few Myr. Varying as well as the size-dependent non-collisional removal rates from the main belt, within reasonable ranges, we are able to obtain main belt and NEA populations in our model, which we can compare with the observed main belt and NEA size distributions. In addition, we can compare the collisional lifetimes of meter-sized bodies in our model with the CRE ages of meteorites, and we can see if the main belt population we obtain is consistent with the cratering records on observed asteroids. Results: Figure 1 shows the main belt population obtained from our collisional model, compared with the observed main belt population determined from direct observation and debiased Spacewatch [3] and Sloan Digital Sky Survey data [4]. Model NEA Population Model MB Population