Impact Mechanics and Frequency of SL9-Type Events on Jupiter

A semianalytic model for the breakup of fragments of Comet Shoemaker-Levy 9 upon entry into Jupiter's atmosphere is presented. The model assumes that the impacting fragments behave as bodies of viscous fluid and that the dominant process in their breakup is the growth of hydrodynamic instabilities. It is shown that the size of the smallest instabilities that contribute to mass loss largely determines the depth of penetration in a way which is consistent with the changes in penetration depth obtained using numerical models with different resolutions. If the diameter of the impactor corresponds to 8 resolution elements then the penetration depths obtained are about 10 ²km too large. To obtain penetration depths within one scale height (≈25 km) of the viscosity limited value, at least 25 resolution elements are required across the diameter of the impactor. This result is in agreement with the numerical studies of K. Zahnle and M.-M. Mac Low (1994, Icarus108, 1-17). It is also shown that two different regimes of hydrodynamic mass loss exist, one caused by Kelvin-Helmholtz (KH) type instabilities and a later one caused by the onset of Rayleigh-Taylor (RT) type instabilities. These regimes can be identified in the numerical results of D. A. Crawford et al. (1994, Shock Waves4, 47-50), where KH instabilities appear to be the major mass loss mechanism between 100 and 200 km below 1 bar and RT instabilities become dominant below 200 km below 1 bar. The upward velocity of material behind the shock caused by the expansion of the superheated gas in the Comet's wake is then calculated and shown to be about 12 km sec ^-1and, to a first approximation, independent of the size of the impacting fragment provided that the fragment is not significantly decelerated before it reaches the tropopause (100 mbar). This upward velocity implies a plume height of 3000 km above the 1-bar level, which agrees with Hubble Space Telescope observations. It is shown that for no significant deceleration to occur before the tropopause the impacting fragments that produced plumes must have had diameters larger than 0.3 km. This, in turn, implies a progenitor diameter of 1.6 km. It is then estimated that the time interval between impacts of 0.3 km diameter comets on Jupiter is approximately 500 years, whereas the interval between the impact of 1.6 km comets is about 6000 years.