Why the SL9 Plumes Were All About the Same Height

Several of the SL9 ejecta plumes were observed by the HST to reach approximately the same height, about 3000 km above the jovian cloud tops. The duration of the infrared events, which were produced by the plume falling back on the atmosphere, measures time aloft and hence provides a second, more sensitive measure of plume height; the light curves indicate that the largest impacts produced modestly higher plumes. Evidently these plumes were launched with about the same vertical velocity, roughly 10-13 kilometers per second. As the impactors themselves were not all the same, nor the impacts equally luminous, nor the plumes equally opaque, the similar plume heights has been seen as a puzzle needing explanation. A second, closely related matter that needs to addressed quantitatively is the popular contention that a big plume requires a big impact. This view is misleading at best, yet plume heights can be used to constrain impact parameters. Dimensional analysis indicates that plume height goes as z alpha v (sup 2) (sub ej) alpha E/pH (sup 2), where v (sub ej) is the ejection velocity, E the explosion energy, and p and H the ambient pressure and scale height at termination. Using a semi-analytic model for the deceleration, disintegration, and destruction of intruding bodies by an ever-vigilant atmosphere, we find that the ratio E/pH(sup 2) is roughly constant for fragments with diameters of order 100 m to 1000 m. Constancy of v(sub ej) is in part due to the greater role of radiative ablation on the flight of smaller objects. We conclude that similar plume heights is a direct consequence of smaller impactors exploding at higher altitudes, in such a way that the different explosions were geometrically similar.