A fundamental, unsolved problem in Solar System formation is explaining the melting and crystallization of chondrules found in chondritic meteorites. Theoretical models of chondrule melting in nebular shocks has been shown to be consistent with many aspects of thermal histories inferred for chondrules from laboratory experiments; but, the mechanism driving these shocks is unknown. Planetesimals and planetary embryos on eccentric orbits can produce bow shocks as they move supersonically through the disk gas, and are one possible source of chondrule-melting shocks. We investigate chondrule formation in bow shocks around planetoids through 3D radiation hydrodynamics simulations. A new radiation transport algorithm that combines elements of flux-limited diffusion and Monte Carlo methods is used to capture the complexity of radiative transport around bow shocks. An equation of state that includes the rotational, vibrational, and dissociation modes of H$_2$ is also used. Solids are followed directly in the simulations and their thermal histories are recorded. Adiabatic expansion creates rapid cooling of the gas, and tail shocks behind the embryo can cause secondary heating events. Radiative transport is efficient, and bow shocks around planetoids can have luminosities $sim$few$times10^{-8}$ L$_{odot}$. While barred and radial chondrule textures could be produced in the radiative shocks explored here, porphyritic chondrules may only be possible in the adiabatic limit. We present a series of predicted cooling curves that merit investigation in laboratory experiments to determine whether the solids produced by bow shocks are represented in the meteoritic record by chondrules or other solids.
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