In the new paper Chen & Lin (2018), my summer student Jhih-Wei Chen conducted numerical simulations to investigate the effect of dust on disc-planet interaction, with focus on disc-planet torques. To model a dusty disc, we modified the PLUTO hydrodynamics code to evolve the dust via an effective energy equation, as detailed in Lin & Youdin (2017).
For perfectly coupled dust particles (dashed curve in the left figure), the disc-planet torques match well to those predicted by the semi-analytic formula of Paardekooper et al. (2010), which are based on pure gas simulations. In the limit of perfect coupling, the presence of dust only rescales the torques, while the qualitative behavior is similar to pure gas discs: torques oscillate but eventually damp to a constant value.
However, for partially coupled dust particles we found a different behavior: torques remain oscillatory for an extended period of time before damping (solid curve in the torque plot). Furthermore, the disc response to the planet is quite different to that with perfectly coupled dust. As the top figure shows, a `bubble' is created inside the planet's co-orbital region, which is responsible for oscillatory torques. We discuss possible consequences of these torque oscillations in dusty discs, including eccentricity excitation.
In the Appendices we also present other test calculations to demonstrate Lin & Youdin's dust-free framework can produce previous, well-known results in dusty protoplanetary discs, including dust trapping at planet gap edges, dust settling, and the streaming instability.
For full details, read the paper here.