  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 suggest
inhomogeneous heating of the outer disk in azimuth, leading to a "thermal
forcing" with dynamical consequences. We conduct a suite of idealized 2D 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. Towards 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 call for more detailed modeling
incorporating more realistic disk physics.
