On shocks driven by high-mass planets in radiatively inefficient disks. II. Three-dimensional global disk simulations

Recent high-resolution, near-infrared images of protoplanetary disks have shown that these disks often present spiral features. Spiral arms are among the structures predicted by models of disk-planet interaction and thus it is tempting to suspect that planetary perturbers are responsible for these signatures. However, such interpretation is not free of problems. The observed spirals have large pitch angles, and in at least one case (HD 100546) it appears effectively unpolarized, implying thermal emission of the order of 1000 K (465 +/- 40 K at closer inspection). We have recently shown in two-dimensional models that shock dissipation in the supersonic wake of high-mass planets can lead to significant heating if the disk is sufficiently adiabatic. Here we extend this analysis to three dimensions in thermodynamically evolving disks. We use the Pencil Code in spherical coordinates for our models, with a prescription for thermal cooling based on the optical depth of the local vertical gas column. We use a 5MJ planet, and show that shocks in the region around the planet where the Lindblad resonances occur heat the gas to substantially higher temperatures than the ambient gas. The gas is accelerated vertically away from the midplane to form shock bores, and the gas falling back toward the midplane breaks up into a turbulent surf. This turbulence, although localized, has high a values, reaching 0.05 in the inner Lindblad resonance, and 0.1 in the outer one. We find evidence that the disk regions heated up by the shocks become superadiabatic, generating convection far from the planet's orbit.