A Shock Heating Model for Chondrule Formation in a Protoplanetary Disk

Abstract

Chondrule formation due to the shock heating of dust particles with a wide variety of shock properties are examined. We numerically simulate the steady postshock region in a framework of one-dimensional hydrodynamics, taking into account many of the physical and chemical processes that determine the properties of the region, especially nonequilibrium chemical reactions of gas species. We mainly focus on the maximum temperature of dust particles and their net cooling rate in relation to the chondrule formation. We derive the condition of chondrule formation for the shock velocity v s and the preshock density n 0. For n 0>10 14.5 cm −3, the shock velocity should be in a range 6 km s −1≤ v s ≤7 km s −1, while for n 0<10 14.5 cm −3, v s should be 6×( n 0/10 14.5 cm −3) −1/5 km s −1≤ v s ≤7×( n 0/10 14.5 cm −3) −1/5 km s −1 for an initial dust particle radius of 0.1 mm. The condition has a small dependence on particle size. We find that the Keplerian velocities and equatorial plane densities around the asteroidal and Jupiter orbital regions of the minimum mass solar nebula model are suitable for chondrule formation. We also find that the gas pressure in the postshock region is much higher than the one in the standard nebula environment. Furthermore, we find that the net cooling rates of 0.1–1-mm-sized dust particles are about 10 2−10 5 K h −1, which are not too far from experimental values, though the melting region is optically thin. Those slow net cooling rates are maintained by drag heating in the cooling phase. These results indicate that the shock heating model can be regarded as a strong candidate for the mechanism of chondrule formation.