Chondrule formation in bow shocks around eccentric planetary embryos

Recent isotopic studies of Martian meteorites by Dauphas & Pourmand have established that large (3000km radius) planetary embryos existed in the solar nebula at the same time that chondrules - millimeter-sized igneous inclusions found in meteorites - were forming. We model the formation of chondrules by passage through bow shocks around such a planetary embryo on an eccentric orbit. We numerically model the hydrodynamics of the flow and find that such large bodies retain an atmosphere with Kelvin-Helmholtz instabilities allowing mixing of this atmosphere with the gas and particles flowing past the embryo. We calculate the trajectories of chondrules flowing past the body and find that they are not accreted by the protoplanet, but may instead flow through volatiles outgassed from the planet's magma ocean. In contrast, chondrules are accreted onto smaller planetesimals. We calculate the thermal histories of chondrules passing through the bow shock. We find that peak temperatures and cooling rates are consistent with the formation of the dominant, porphyritic texture of most chondrules, assuming a modest enhancement above the likely solar nebula average value of chondrule densities (by a factor of 10), attributable to settling of chondrule precursors to the midplane of the disk or turbulent concentration. We calculate the rate at which a planetary embryo's eccentricity is damped and conclude that a single planetary embryo scattered into an eccentric orbit can, over 10⁵years, produce 10²⁴ g of chondrules. In principle, a small number (1-10) of eccentric planetary embryos can melt the observed mass of chondrules in a manner consistent with all known constraints.