Starlight-driven flared-staircase geometry in radiation hydrodynamic models of protoplanetary disks

Abstract: Protoplanetary disks observed in millimeter continuum and scattered light show a variety of substructures. Various physical processes in the disk could trigger such features -- one of which that has been previously theorized for passive disks is the thermal wave instability -- the flared disk may become unstable as directly illuminated regions puff up and cast shadows behind them. This would manifest as bright and dark rings, and a staircase-like structure in the disk optical surface. We provide a realistic radiation hydrodynamic model to test the limits of the thermal wave instability in irradiated disks. We carry out global axisymmetric 2D hydrostatic and dynamic simulations including radiation transport with frequency-dependent ray-traced irradiation and flux-limited diffusion (FLD). We found that starlight-driven shadows are most prominent in optically thick, slow cooling disks, shown by our models with high surface densities and dust-to-gas ratios of sub-micron grains of 0.01. We recover that thermal waves form and propagate inwards in the hydrostatic limit. In contrast, our hydrodynamic models show bumps and shadows within 30 au that converge to a quasi-steady state on several radiative diffusion timescales -- indicating a long-lived staircase structure. We find that existing thermal pressure bumps could produce and enhance this effect, forming secondary shadowing downstream. Hydrostatic models with self-consistent dust settling instead show a superheated dust irradiation absorption surface with a radially smooth temperature profile without staircases. We conclude that one can recover thermally induced flared-staircase structures in radiation hydrodynamic simulations of irradiated protoplanetary disks using flux-limited diffusion. We highlight the importance of modeling dust dynamics consistently to explain starlight-driven shadows.