Thermal waves in protoplanetary disks and the resultant change of SED.

Abstract

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. We calculate the quasi-static thermal evolution of irradiated disks by directly integrating the 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 the instability and an approximately steady state is realized throughout the disk. In passive protostellar disks, these waves induce a significant change in SEDs because the midplane temperatures can vary by a factor of two between the exposed and shadowed regions.