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Evolution of Coated Grains in Spiral Shocks of Self-Gravitating Protoplanetary Disks

We investigate the evolution of grains composed of an ice shell surrounding an olivine core as they pass through a spiral shock in a protoplanetary disk. We use published three-dimensional radiation-hydrodynamics simulations of massive self-gravitating protoplanetary disks to extract the thermodynamics of spiral shocks in the region between 10 and 20 AU from the central star. As the density wave passes, it heats the grains, causing them to lose their ice shell and resulting in a lowering of the grain opacity. In addition, since grains of different sizes will have slightly different temperatures, there will be a migration of ice from the hotter grains to the cooler ones. The rate of migration depends on the temperature of the background gas, so a grain distribution that is effectively stable for low temperatures, can undergo an irreversible change in opacity if the gas is temporarily heated to above $\sim 150$\,K. We find that the opacity can drop more, and at a significantly faster rate throughout the spiral shocks relative to the prediction of standard dust grains models adopted in hydrodynamical calculations of protoplanetary disks. This would lead to faster gas cooling within spiral arms. We discuss the implications of our results on the susceptibility of disk fragmentation into sub-stellar objects at distances of a few tens of astronomical units.