Radiative Scale Height and Shadows in Protoplanetary Disks

Planets form in young circumstellar disks called protoplanetary disks. However, it is still difficult to catch planet formation in situ. Nevertheless, from recent ALMA/SPHERE data, encouraging evidence of the direct and indirect presence of embedded planets has been identified in disks around young stars: co-moving point sources, gravitational perturbations, rings, cavities, and emission dips or shadows cast on disks. The interpretation of these observations needs a robust physical framework to deduce the complex disk geometry. In particular, protoplanetary disk models usually assume the gas pressure scale height given by the ratio of the sound speed over the azimuthal velocity H/r = cs/vk. By doing so, radiative pressure fields are often ignored, which could lead to a misinterpretation of the real vertical structure of such disks. We follow the evolution of a gaseous disk with an embedded Jupiter-mass planet through hydrodynamical simulations, computing the disk scale height including radiative pressure, which was derived from a generalization of the stellar atmosphere theory. We focus on the vertical impact of the radiative pressure in the vicinity of circumplanetary disks, where temperatures can reach ≳1000 K for an accreting planet and radiative forces can overcome gravitational forces from the planet. The radiation pressure effects create a vertical, optically thick column of gas and dust at the protoplanet location, casting a shadow in scattered light. This mechanism could explain the peculiar illumination patterns observed in some disks around young stars such as HD 169142 where a moving shadow has been detected or the extremely high aspect ratio H/r ∼ 0.2 observed in systems like AB Aur and CT Cha.