A semiempirical model of catastrophic breakup processes

Several observable properties of asteroids, including their sizes, shapes, and rotations, are the direct outcome or are in some way connected with catastrophic breakup events caused by high-velocity impacts. On a much smaller scale, these catastrophic impacts have been investigated in the laboratory, but a comprehensive physical theory of the fragmentation phenomenon is not yet available. We have attempted to reinterpret the results of laboratory impact experiments as well as the asteroids properties in terms of a semiempirical theory which derives the observable properties of the fragments from a suitable velocity field of the target material, assumed to arise from the explosion due to the impact and from the original rotation of the target. Apart from this latter term (which is usually smaller), the field is essentially radial (though not central) and in terms of it we have defined a “local” breakup criterion and derived the size, bulk velocity, shape, and rotation of the final fragments. Numerical simulations based on the idea of studying the local fragment properties as a function of initial position in the target have allowed us to compare the results of this model (varying several free parameters) with the experimental results and, in a few cases, with asteroid properties. In particular, the fragment rotation is found to arise from the superposition of two effects, one due to the curl of the velocity field and the other to the asphericity of the fragment shapes. Some observed properties of the main asteroid families (the likely outcomes of asteroidal catastrophic collisions) are well reproduced by the model, and observable correlations among ejection velocity, size, rotation, and shape can be predicted.