Effects of the geometric constraints on the size distributions of debris in asteroidal fragmentation

It is commonly accepted that the formation of asteroid families is the cons equence of catastrophic impacts on former parent bodies: (K. Hirayama, Proc . Imp. Acad. Tokyo 9, 482-485, 1933). But to reproduce the puzzling steep s ize distributions of the currently known asteroid families has been, up to now a task in which recent modeling techniques of fragmentation have typica lly failed. The role of geometric constraints in the production of fragment s in asteroidal collisions is an issue that has been investigated in recent times only by Tanga ct al. (Icarus 141, 65-78, 1999) and that might give s ome insight into the understanding of high-velocity collisional processes., Improvements to the approach by Tanga ct al. are introduced in the present work in order to take into account in a more realistic way the different s hapes that the largest remnants may have when formed in high-velocity colli sional events involving spherical parent bodies. We also consider the case in which the parent body and the largest remnant are cubes and the fragment s are (a) cubes and (b) parallelepipeds, instead of spheres. A somewhat uni form power-law behavior in the size;distributions of the randomly generated fragments is found in the numerical simulations-not detected by Tanga et a l.-and an analytical derivation of the upper limit to the corresponding exp onent is given. Further improvements are introduced in the model in order t o refine it and allow any fragment to develop any shape and to account for the fact that fragments form more or less at the same time, not sequentiall y. Finally, the results of the refined model are compared with the size dis tributions of the observed actual main belt asteroid families, and encourag ing agreement is obtained in most cases. (C) 2000 Academic Press.