Simulation of Thermal Surface Waves in a Protoplanetary Disk in 1+1D Approximation

Abstract

Heating by the central star is one of the key factors determining the physical structure of protoplanetary disks. Due to a large radial optical thickness, the equatorial regions of the disk are heated by infrared radiation from the disk surface (atmosphere), which in turn is heated by the direct radiation from the star. It was previously shown that interception of the stellar radiation by inhomogeneities on the disk surface can cause perturbations that propagate towards the star. In this work, within a detailed 1+1D-dimensional numerical model of a protoplanetary disk, the occurrence of such waves is studied. It was found that, in a disk that is optically thick to its own radiation, surface perturbations indeed form and propagate towards the star, which confirms the conclusions of other authors. However, in contrast to analytical predictions, we found that, for sufficiently massive disks, thermal waves affect only the upper layers without significant temperature fluctuations in the equatorial plane. The results obtained indicate the need to study this instability within more consistent hydrodynamic models.