  Protoplanetary disks are mainly heated by radiation from the central star.
Since the incident stellar flux at any radius is sensitive to the disk
structure near that location, an unstable feedback may be present. Previous
investigations show that the disk would be stable to finite-amplitude
temperature perturbations if the vertical height of optical surface is
everywhere directly proportional to the gas scale height and if the intercepted
fraction of stellar radiation is determined from the local grazing angle. We
show that these assumptions may not be generally applicable. Instead, we
calculate the quasi-static thermal evolution of irradiated disks by directly
integrating the global optical depths to determine the optical surface and the
total emitting area-filling factor of surface dust. We show that, in disks with
modest mass accretion rates, thermal waves are spontaneously and continually
excited in the outer disk, propagate inward through the planet-forming domains,
and dissipated at small radii where viscous dissipation is dominant. This state
is quasi-periodic over several thermal timescales and its pattern does not
depend on the details of the opacity law. The viscous dissipation resulting
from higher mass accretion stabilizes this instability such that an
approximately steady state is realized throughout the disk. In passive
protostellar disks, especially transitional disks, these waves induce
significant episodic changes in SEDs, on the time scales of years to decades,
because the midplane temperatures can vary by a factor of two between the
exposed and shadowed regions. The transitory peaks and troughs in the potential
vorticity distribution may also lead to baroclinic instability and excite
turbulence in theplanet-forming regions.
