Irradiated Disks May Settle into Staircases

Much of a protoplanetary disk is thermally controlled by irradiation from the central star. Such a disk, long thought to have a smoothly flaring shape, is unstable due to the so-called irradiation instability. But what is the outcome of such an instability? In particular, is it possible that such a disk settles into a shape that is immune to the instability? We combine Athena++ with a simplified thermal treatment to show that passively heated disks settle into a staircase shape. Here, the disk is punctuated by bright rings and dark gaps, with the bright rings intercepting the lion’s share of stellar illumination, and the dark gaps are hidden in their shadows. The optical surface of such a disk (the height at which starlight is absorbed) resembles a staircase. Although our simulations do not have realistic radiative transfer, we use the RADMC-3D code to show that this steady state is in good thermal equilibrium. It is possible that realistic disks reach such a state via ways not captured by our simulations. In contrast to our results here, two previous studies have claimed that irradiated disks stay smooth. We show here that they err on different issues. The staircase state, if confirmed by more sophisticated radiative hydrodynamic simulations, has a range of implications for disk evolution and planet formation.