The nebular shock wave model for chondrule formation: Shock processing in a particle-gas suspension

We present numerical simulations of the thermal and dynamical histories of solid particles (chondrules and their precursors-treated as 1-mm silicate spheres) during passage of an adiabatic shock wave through a particle-gas suspension in a minimum-mass solar nebula. The steady-state equations of energy, momentum, and mass conservation are derived and integrated for both solids and gas under a variety of shock conditions and particle number densities using the free-molecular-flow approximation. These simulations allow us to investigate both the heating and cooling of particles in a shock wave and to compare the time and distance scales associated with their processing to those expected for natural chondrules. The interactions with the particles cause the gas to achieve higher temperatures and pressures both upstream and downstream of the shock than would be reached otherwise. The cooling rates of the particles are found to be nonlinear but agree approximately with the cooling rates inferred for chondrules by laboratory simulations. The initial concentration of solids upstream of the shock controls the cooling rates and the distances over which they are processed: Lower concentrations cool more slowly and over longer distances. These simulations are consistent with the hypothesis that large-scale shocks, e.g., those due to density waves or gravitational instabilities, were the dominant mechanism for chondrule formation in the nebula. (C) 2002 Elsevier Science (USA).