The Structure of Spiral Shocks Excited by Planetary-mass Companions
Zhu et al
Recent direct imaging observations have revealed spiral structure in protoplanetary disks. Previous studies have suggested that planet-induced spiral arms cannot explain these spiral patterns, as 1) the pitch angle of the spiral arm is larger in observations than that predicted by the linear density wave theory, 2) the contrast of the spiral arm is higher in observations than in synthetic observations based on two dimensional planet-disk simulations. We have carried out three dimensional (3-D) hydrodynamical simulations to study spiral wakes/shocks excited by young planets. We find that, in contrast with linear theory, the pitch angle of spiral arms does depend on the planet mass, which can be explained by the non-linear density wave theory. The more massive is the planet, the larger pitch angle the spiral arm has. A secondary spiral arm, especially for the inner arms, is also excited by the planet. The more massive is the planet, the larger is the separation in the azimuthal direction between the primary and secondary arms. We also find that although the arms in the outer disk do not exhibit much vertical motion, the inner arms have significant vertical motion, which boosts the density perturbation at the disk atmosphere by more than a factor of 10 compared with that at the disk midplane. Combining hydrodynamical models with Monte-Carlo radiative transfer calculations, we find that the inner spiral arms are considerably more prominent in synthetic near-IR images using full 3-D hydrodynamical models than images based on 2-D models, indicating the need to model observations with full 3-D hydrodynamics. Overall, spiral arms (especially inner arms) excited by planetary-mass objects are prominent features that are observable by current near-IR imaging facilities, and the shape of the spiral arms informs us not only about the position but also about the mass of the companion.