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Two-fluid dusty shocks: simple benchmarking problems and applications to protoplanetary discs

The key role that dust plays in the interstellar medium has motivated the development of numerical codes designed to study the coupled evolution of dust and gas in systems such as turbulent molecular clouds and protoplanetary discs. Drift between dust and gas has proven to be important as well as numerically challenging. We provide simple benchmarking problems for dusty gas codes by numerically solving the two-fluid dust-gas equations for steady, plane-parallel shock waves. The two distinct shock solutions to these equations allow a numerical code to test different forms of drag between the two fluids, the strength of that drag and the dust to gas ratio. We also provide an astrophysical application of J-type dust-gas shocks to studying the structure of accretion shocks onto protoplanetary discs. We find that two-fluid effects are most important for grains larger than 1 um, and that the peak dust temperature within an accretion shock provides a signature of the dust-to-gas ratio of the infalling material.