IMPACT MECHANICS AND FREQUENCY OF SL9-TYPE EVENTS ON JUPITER

A semianalytic model for the breakup of fragments of Comet Shoemaker-L evy 9 upon entry into Jupiter's atmosphere is presented. The model ass umes that the impacting fragments behave as bodies of viscous fluid an d that the dominant process in their breakup is the growth of hydrodyn amic instabilities. It is shown that the size of the smallest instabil ities that contribute to mass loss largely determines the depth of pen etration in a way which is consistent with the changes in penetration depth obtained using numerical models with different resolutions, If t he diameter of the impactor corresponds to 8 resolution elements then the penetration depths obtained are about 10(2) km too large, To obtai n penetration depths within one scale height (approximate to 25 km) of the viscosity limited value, at least 25 resolution elements are requ ired across the diameter of the impactor. This result is in agreement with the numerical studies of K. Zahnle and M.-M. Mac Low (1994, Icaru s 108, 1-17). It is also shown that two different regimes of hydrodyna mic mass loss exist, one caused by Kelvin-Helmholtz (KH) type instabil ities and a later one caused by the onset of Rayleigh-Taylor (RT) type instabilities. These regimes can be identified in the numerical resul ts of D. A. Crawford ct al. (1994, Shock Waves 4, 47-50), where KH ins tabilities appear to be the major mass loss mechanism between 100 and 200 km below 1 bar and RT instabilities become dominant below 200 km b elow 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 calc ulated and shown to be about 12 Ina sec(-1) and, to a first approximat ion, independent of the size of the impacting fragment provided that t he fragment is not significantly decelerated before it reaches the tro popause (100 mbar). This upward velocity implies a plume height of 300 0 km above the 1-bar level, which agrees with Hubble Space Telescope o bservations. It is shown that for no significant deceleration to occur before the tropopause the impacting fragments that produced plumes mu st have had diameters larger than 0.3 km. This, in turn, implies a pro genitor diameter of 1.6 km. It is then estimated that the time interva l between impacts of 0.3 km diameter comets on Jupiter is approximatel y 500 years, whereas the interval between the impact of 1.6 km comets is about 6000 years. (C) 1997 Academic Press.