Dynamical Consequence of Shadows Cast to the Outer Protoplanetary Disks. I. Two-dimensional Simulations

There has been increasing evidence of shadows from scattered light observations of outer protoplanetary disks (PPDs) cast from the (unresolved) disk inner region, while in the meantime these disks present substructures of various kinds in the submillimeter. As stellar irradiation is the primary heating source for the outer PPDs, the presence of such shadows thus suggests inhomogeneous heating of the outer disk in azimuth, leading to a "thermal forcing" with dynamical consequences. We conduct a suite of idealized two-dimensional disk simulations of the outer disk with azimuthally varying cooling prescription to mimic the effect of shadows, generally assuming the shadow is static or slowly rotating. The linear response to such shadows is two-armed spirals with the same pattern speed as the shadow. Toward the nonlinear regime, we find that shadows can potentially lead to the formation of a variety of types of substructures including rings, spirals, and crescents, depending on viscosity, cooling time, etc. We have conducted systematic and statistical characterization of the simulation suite, and as thermal forcing from the shadow strengthens, the dominant form of shadow-induced disk substructures change from spirals to rings, and eventually to crescents/vortices. Our results highlight the importance of properly modeling the dynamical impact of inhomogeneous stellar irradiation, while calling for more detailed modeling incorporating more realistic disk physics.