The Nebular Shock Wave Model for Chondrule Formation: One-Dimensional Calculations

Abstract

We present numerical simulations of the interaction of a one-dimensional radiative gas dynamic shock wave with a dust cloud in the solar nebula that is finite in dimension parallel to the direction of shock propagation. Energy and momentum transfer to the shock-heated gas as the gas penetrates the dust cloud is computed at each time step as well as grain heating due to molecular collisions and radiation from shocked gas and radiation from surrounding dust grains. For all explicit calculations, the dust cloud is composed of equal-sized (1 mm radius) silicate grains and the nebula gas has an initial number density of 1014 cm-3 and a temperature of 500 K. For the case of a marginally optically thick dust cloud (half thickness 100 km and dust number density 3.2 grains m-3), shock Mach numbers >3.1 are sufficient to bring a small fraction of grains within the cloud to the melting temperature while Mach numbers >4 are sufficient to melt most grains in the cloud. Larger dust densities (optical depth ⪢1) result in more rapid melting of grains near the upstream edge of the dust cloud but grains in the interior are relatively shielded from drag heating due to momentum loss by the shocked gas. For initial nebula number densities greater (smaller) than 1014 cm-3, smaller (larger) Mach numbers are required to melt grains. Nonspherical (e.g., fractal) grains would reach melting temperatures for smaller Mach numbers at a given initial nebula density and temperature. More detailed calculations for a continuous size distribution of dust grains may provide a means of understanding the observed narrow range of chondrule sizes.