Thermal processing of chondrule precursors in planetesimal bow shocks

We test the hypothesis that chondrules (and Type B and C calcium-aluminum-rich inclusions, CAIs) originated during passage of precursors through bow shocks upstream of planetesimals moving supersonically relative to nebula gas. A two-dimensional piecewise parabolic method (PPM) hydrocode, supplemented by a one-dimensional adiabatic shock model, is employed to simulate the postshock gas density, temperature, and velocity fields for given planetesimal sizes, velocities, and ambient nebular densities and temperatures. Thermal histories of incident silicate particles are calculated in the free molecular flow approximation by integration of the one-dimensional equations of gas-grain energy and momentum transfer. For gas number densities >10(14) cm(-3), Mach numbers in the range of 4 to 5 are sufficient to melt isolated spherical particles with radii in the range 0.05 to 0.5 mm during passage of shocked gas thicknesses of 25-35 km. Minimum gas-planetesimal relative velocities are in the range 5.5-7 km/s, implying orbital eccentricities >0.2 and/or inclinations >15 degrees. Melting of centimeter-sized CAI precursors requires either higher Mach numbers (6-7) or ambient gas densities >10(15)cm(-3). For a constant radial distribution of planetesimal orbital eccentricities and inclinations, the model predicts more efficient melting of precursor particles at decreasing radial distances from the Sun where planetesimal velocities are largest. In order to process a significant fraction of solids in the nebula, planetesimals near similar to 2.5 AU during the chondrule formation epoch must have had a range of eccentricities and inclinations comparable to those presently observed in the residual asteroid belt. The most likely energy som ce for maintaining the necessary gas-planetesimal relative velocities is external gravitational perturbations associated with the forming outer planets, primarily Jupiter.