Hydrodynamical simulations of protoplanetary disks including irradiation of stellar photons. I. Resolution study for Vertical Shear Instability (VSI)

Abstract: In recent years hydrodynamical (HD) models have become important to describe the gas kinematics in protoplanetary disks, especially in combination with models of photoevaporation and/or magnetic-driven winds. We focus on diagnosing the the vertical extent of the VSI at 203 cells per scale height and allude at what resolution per scale height we obtain convergence. Finally, we determine the regions where EUV, FUV and X-Rays are dominant in the disk. We perform global HD simulations using the PLUTO code. We adopt a global isothermal accretion disk setup, 2.5D (2 dimensions, 3 components) which covers a radial domain from 0.5 to 5.0 and an approximately full meridional extension. We determine the 50 cells per scale height to be the lower limit to resolve the VSI. For higher resolutions, greater than 50 cells per scale height, we observe the convergence for the saturation level of the kinetic energy. We are also able to identify the growth of the `body' modes, with higher growth rate for higher resolution. Full energy saturation and a turbulent steady state is reached after 70 local orbits. We determine the location of the EUV-heated region defined by the radial column density to be 10$^{19}$ cm$^{-2}$ located at $H_\mathrm{R}\sim9.7$, and the FUV/X-Rays-heated boundary layer defined by 10$^{22}$ cm$^{-2}$ located at $H_\mathrm{R}\sim6.2$, making it necessary to introduce the need of a hot atmosphere. For the first time, we report the presence of small scale vortices in the r-Z plane, between the characteristic layers of large scale vertical velocity motions. Such vortices could lead to dust concentration, promoting grain growth. Our results highlight the importance to combine photoevaporation processes in the future high-resolution studies of the turbulence and accretion processes in disks.