  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 to the so-called 'irradiation instability'. But what's 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 hidden in their shadows. The optical surface of such a disk
(height at which starlight is absorbed) resembles a staircase. Although our
simulations do not have realistic radiative transfer, we use the RADMC3d 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.
