The scale size of chondrule formation regions: Constraints imposed by chondrule cooling rates

Meteoritic data strongly suggest that most chondrules reached maximum temperatures in a range of 1650-2000 K and cooled at relatively slow rates of 100-1000 K/h, implying a persistence of external energy supply. The presence of fine-grained rims around chondrules in most unequilibrated chondrites also indicates that a significant quantity of micron-sized dust was present in chondrule formation regions. Here, we assume that the persistent external energy source needed to explain chondrule cooling rates consists primarily of radiation from surrounding heated chondrules, fine dust, and gas after the formation event. Using an approximate one-dimensional numerical model for the outward diffusion of thermal radiation from such a system, the scale sizes of formation regions required to yield acceptable cooling rates are determined for a range of possible chondrule, dust, and gas parameters. Results show that the inferred scale sizes depend sensitively on the number densities of micron-sized dust and on their adopted optical properties. In the absence of dust, scale sizes >1000 km are required for plausible maximum chondrule number densities and heated gas parameters. In the presence of dust with mass densities comparable to those of the chondrules and with absorptivities and emissivities of ~0.01 calculated for Mie spheres with a pure mineral composition, scale sizes as small as ~100 km are possible. If dust absorptivities and emissivities approach unity (as may occur for particles with more realistic shapes and compositions), then scale sizes as small as ~10 km are possible. Considering all uncertainties in model parameters, it is concluded that small scale sizes (10-100 km) for chondrule formation regions are allowed by the experimentally inferred cooling rates.