  Theoretical models of protoplanetary disks including stellar irradiation
often show a spontaneous amplification of scale height perturbations, produced
by the enhanced absorption of starlight in enlarged regions. In turn, such
regions cast shadows on adjacent zones that consequently cool down and shrink,
eventually leading to an alternating pattern of overheated and shadowed
regions. Previous investigations have proposed this to be a real self-sustained
process, the so-called self-shadowing or thermal wave instability, which could
naturally form frequently observed disk structures such as rings and gaps, and
even potentially enhance the formation of planetesimals. All of these, however,
have assumed in one way or another vertical hydrostatic equilibrium and
instantaneous radiative diffusion throughout the disk. In this work we present
the first study of the stability of accretion disks to self-shadowing that
relaxes these assumptions, relying instead on radiation-hydrodynamical
simulations. We first construct hydrostatic disk configurations by means of an
iterative procedure and show that the formation of a pattern of enlarged and
shadowed regions is a direct consequence of assuming instantaneous radiative
diffusion. We then let these solutions evolve in time, which leads to a fast
damping of the initial shadowing features in layers close to the disk surface.
These thermally relaxed layers grow towards the midplane until all temperature
extrema in the radial direction are erased in the entire disk. Our results
suggest that radiative cooling and gas advection at the disk surface prevent a
self-shadowing instability from forming, by damping temperature perturbations
before these reach lower, optically thick regions.
