A model of the thermal processing of particles in solar nebula shocks: Application to the cooling rates of chondrules

We present a model for the thermal processing of particles in shock waves typical of the solar nebula. This shock model improves on existing models in that the dissociation and recombination of H₂ and the evaporation of particles are accounted for in their effects on the mass, momentum and energy fluxes. Also, besides thermal exchange with the gas and gas-drag heating, particles can be heated by absorbing the thermal radiation emitted by other particles. The flow of radiation is calculated using the equations of radiative transfer in a slab geometry. We compute the thermal histories of particles as they encounter and pass through the shock. We apply this shock model to the melting and cooling of chondrules in the solar nebula. We constrain the combinations of shock speed and gas density needed for chondrules to reach melting temperatures, and show that these are consistent with shock waves generated by gravitational instabilities in the protoplanetary disk. After their melting, cooling rates of chondrules in the range 10-1000 K h⁻¹ are naturally reproduced by the shock model. Chondrules are kept warm by the reservoir of hot shocked gas, which cools only as fast as the dust grains and chondrules themselves can radiate away the gas's energy. We predict a positive correlation between the concentration of chondrules in a region and the cooling rates of chondrules in that region. This correlation is supported by the unusually high frequency of (rapidly cooled) barred chondrules among compound chondrules, which must have collided preferentially in regions of high chondrule density. We discuss these and other compelling consistencies between the meteoritic record and the shock wave model of chondrule formation.