Simulation of Thermal Surface Waves in a Protoplanetary Disk in a Two-Dimensional Approximation

Theoretical models predict that the obscuration of stellar radiation by irregularities on the surface of a protoplanetary disk can cause self-generating waves traveling towards the star. However, this process is traditionally simulated using the 1+1D approach, the key approximations of which - vertical hydrostatic equilibrium of the disk and vertical diffusion of IR radiation - can distort the picture. This article presents a two-dimensional radiative hydrodynamic model of the evolution of an axially symmetric gas and dust disk. Within this model, but using simplified assumptions from 1+1D models, we have reproduced the spontaneous generation and propagation of thermal surface waves. The key conclusion of our work is that taking into account two-dimensional hydrodynamics and diffusion of IR radiation suppresses the spontaneous generation and development of thermal waves observed in the 1+1D approximation. The search for the possibility of the existence of surface thermal waves should be continued by studying the problem for various parameters of protoplanetary disks.