Donald R. Davis

Asteroid collisional evolution: results from current scaling algorithms

Abstract Acritical element for the understanding of asteroid collisional evolution is the scaling law needed to link laboratory impact experiments to the fragmentation of asteroidal bodies, ranging in size from meters to several hundreds of km. Early workers generally assumed a simple energy scaling, augmented by gravitational self-compression. Recent work on scaling theories has produced algorithms for computing the specific energy, Q ∗ , required to fragment bodies of various sizes, based on two approaches: the strain-rate scaling theory of Housen and Holsapple (Icarus, 84, 226, 1990), based on dimensional analysis, and the 2-D hydrocode ealculations of Ryan and Melosh (1994). The strain-rate scaling predicts a deerease of about an Order of magnitude when going from laboratory sized bodies, 10 cm, to bodies a few tens of km in size, whereas for larger sizes Q ∗ , grows due to gravitational self- compression. The hydrocode results show an even stronger dependence on size, with a Q ∗ decrease of 2–3 orders of magnitude between 10 cm and 25 km, depending on the properties of the material. One possible way to discriminate among these different scaling laws is to examine which of them (if any) can predict the observed size distribution of asteroids from arbitrary starting populations and simultaneously satisfy other constraints on asteroid collisional history, such as the preservation of Vestas basaltic crust. We have now explored this problem using the asteroid collisional evolution model of Davis et al. (AsteroidsII, pp. 805–826, University of Arizona Press, Tuscon, 1989), modified to take the different scaling algorithms as an input option. These model calculations show that a comparatively large value of Q ∗ is neede to match the observed size distribution and to preserve Vestas crust. Simple energy scaling with gravitational self-compression in agreement with the laboratory experiments of Housen et al. (Iearus94, 180, 1991) does the best of reproducing the observed asteroid belf. Strain-rate scaling could also match the observations; however, extension of our knowledge of the main-belt population down to sizes of ∼ 1 km would test this agreement. The hydrocode scaling results generally predict weak asteroids and do not reproduce the size distribution, nor do they allow Vestas crust to be preserved except in a highly improbable fashion. The hydrocode scaling of Q ∗ however, provides only a shattering threshold; work to derive the corresponding scaling law for the energy partitioning coefficient, needed to model the dispersal/reaccumulation of fragments, is under way.