Hydrodynamical Simulations Of Protoplanetary Disks Including Irradiation Of Stellar Photons: I. Resolution Study For Vertical Shear Instability

Context. 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 magnetically driven winds. Our aim is to investigate how vertical shear instability (VSI) could influence the thermally driven winds on the surface of protoplanetary disks.Aims. In this first part of the project, we focus on diagnosing the conditions of the VSI at the highest numerical resolution ever recorded, and suggest at what resolution per scale height we obtain convergence. At the same time, we want to investigate the vertical extent of VSI activity. Finally, we determine the regions where extreme UV (EUV), far-UV (FUV), and X-ray photons are dominant in the disk.Methods. 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. Our simulation runs cover a resolution from 12 to 203 cells per scale height.Results. We determine 50 cells per scale height to be the lower limit to resolve the VSI. For higher resolutions, >= 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 Sigma(r) = 10(19) cm(-2) to be at H-R similar to 9.7 and the FUV-X-ray heated boundary layer defined by Sigma(r) = 10(22) cm(-2) to be at H-R similar to 6.2, making it necessary to introduce 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 of combining photoevaporation processes in the future high-resolution studies of turbulence and accretion processes in disks.