Cometary breakup calculations based on a gravitationally-bound agglomeration model: the density and size of Shoemaker-Levy 9.

By modeling Comet Shoemaker-Levy 9 (1993e) as an agglomeration of identical spherical components, bound together only by gravitation, I obtain several qualitative and quantitative features of the comet's breakup during its close encounter with Jupiter. By comparing the size, number, and spatial distribution of the calculated cometary fragments with observations from the Hubble Space Telescope, I conclude that the density of components should be between 0.5 and 0.6g/cm3. The best qualitative agreement occurs at ρ=0.55g/cm3, which corresponds to a comet average density of about 1/2g/cm3, assuming a face-centered cubic (FCC) initial packing for the components. A much less dense comet will break into fragments that do not gravitationally coalesce into anything resembling the observed string of objects. A much more dense comet may distort or even fracture near perijove, but will quickly coalesce into a single object. Between the limits above, the number of major coalescent fragments decreases rapidly with an increase in density, decreases only slightly with an increase in the assumed number of components, and is relatively insensitive to elasticity within the credible range of variation. The breakup is sensitive to initial rotation of the comet, but the essential results remain the same as for a nonrotating comet as long as the comet's angular velocity is less than 1/3 that required for centrifugal breakup in free space. The model exhibits a remarkable scaling relation that allows a single calculation of the geometric and energetic features to be applied to a comet of any size. Consequently the model can be used to estimate the size of the parent comet, which appears to be about 1.8km in diameter, assuming an initial 321-component FCC bumpy sphere. This diameter is roughly consistent with recent calculations based on the observed plume heights from the fragments after impact.