  Chondrules are important early Solar System materials that can provide a
wealth of information on conditions in the solar nebula, if their formation
mechanism can be understood. The theory most consistent with observational
constraints, especially thermal histories, is the so-called "shock model", in
which chondrules were melted in solar nebula shocks. However, several problems
have been identified with previous shock models. These problems all pertained
to the treatment of the radiation field, namely the input boundary condition to
the radiation field, the proper treatment of the opacity of solids, and the
proper treatment of molecular line cooling. In this paper, we present the
results of our updated shock model, which corrects for the problems listed
above. Our new hydrodynamic shock code includes a complete treatment of
molecular line cooling due to H2O. Previously, shock models including line
cooling predicted chondrule cooling rates exceeding 100,000 K/hr. Contrary to
these expectations, we have found that the effect of line cooling is minimal;
after the inclusion of line cooling, the cooling rates of chondrules are
10-1000 K/hr. The reduction in the otherwise rapid cooling rates attributable
to line cooling is due to a combination of factors, including buffering due to
hydrogen recombination/dissociation, high column densities of water, and
backwarming. Our model demonstrates that the shock model for chondrule
formation remains consistent with observational constraints.
