The transport of thermal radiation in a protostellar envelope

We present a discrete ordinate solution for gray radiation transport in axisymmetric protostellar envelopes, for the purpose of defining the patterns of interstellar-grain survival during the formation of the solar system. The gray transfer problem is nonlinear because the opacity depends on temperature, with discontinuities at temperatures where various species of dust vaporize. The standard lambda iteration techniques that are required for accurate solutions to the transfer equation tend to be nonconvergent under these conditions. We show that accuracy can be achieved through a relaxation method. We first compare the thermal profiles in spherically symmetric envelopes computed by the discrete ordinate solution with those predicted by the diffusion approximation. The more accurate discrete ordinate solutions tend to yield steeper temperature gradients, and the central vaporized cavity around the protostar is larger than that given by the diffusion approximation. The transport solution is then applied to an axisymmetric model envelope in which the cloud is flattened due to rotation, and in which a wind evacuates the polar regions of the cloud. The resulting cavity beams the emergent intensity in the polar direction. When the cloud is uniformly opaque, the polar cavity enhances the diffusive escape of radiation and globally reduces temperatures in the cloud. Modeled temperature profiles are used to predict the radial distances at which various dust, species survive infall in the cloud. The results indicate that survival boundaries range from within 1 AU for the most refractory solids, to several AU for volatile organics, and that water ice is excluded from within 20-30 AU of the protostar during the collapse phase. We compare dust vaporization due to heating in the cloud with destruction in the accretion shock; based on the test case, heating in the cloud during collapse is potentially more destructive.