Models of the Shoemaker-Levy 9 Impacts. I. Ballistic Monte Carlo Plume

We model the plumes raised by impacting fragments of comet Shoemaker-Levy 9 to calculate synthetic plume views, atmospheric infall fluxes, and debris patterns. Our plume is a swarm of ballistic particles with one of several mass-velocity distributions (MVDs). The swarm is ejected instantaneously and uniformly into a cone from its apex. On falling to the ejection altitude, particles slide with horizontal deceleration following one of several schemes. The model ignores hydrodynamic and Coriolis effects. Initial conditions come from observations of plume heights and calculated or estimated properties of impactors. We adjust the plume tilt, opening angle, and minimum velocity and choose MVDs and sliding schemes to create impact patterns that match observations. Our best match uses the power-law MVD from the numerical impact model of Zahnle & Mac Low, with velocity cutoffs at 4.5 and 11.8 km s^-1, a cone opening angle of 75°, a cone tilt of 30° from vertical, and a sliding constant deceleration of 1.74 m s^-2. A mathematically derived feature of Zahnle & Mac Low's published cumulative MVD is a thin shell of mass at the maximum velocity, corresponding to the former atmospheric shock front. This vanguard contains 22% of the mass and 45% of the energy of the plume and accounts for several previously unexplained observations, including the large, expanding ring seen at 3.2 μm by McGregor et al. and the ``third precursors'' and ``flare'' seen near 300 and 1000 s, respectively, in the infrared light curves. We present synthetic views of the plumes in flight and after landing and derive infall fluxes of mass, energy, and vertical momentum as a function of time and position on the surface. These fluxes initialize a radiative-hydrodynamic atmosphere model (Paper II of this series) that calculates the thermal and dynamical response of the atmosphere and produces synthetic light curves.