Modeling of deep gaps created by giant planets in protoplanetary discs

Abstract: A giant planet embedded in a protoplanetary disk creates a gap. This process is important for both theory and observations. Using results of a survey for a wide parameter range with two-dimensional hydrodynamic simulations, we constructed an empirical formula for the gap structure (i.e., the radial surface density distribution), which can reproduce the gap width and depth obtained by two-dimensional simulations. This formula enables us to judge whether an observed gap is likely to be caused by an embedded planet or not. The propagation of waves launched by the planet is closely connected to the gap structure. It makes the gap wider and shallower as compared with the case where an instantaneous wave damping is assumed. The hydrodynamic simulations shows that the waves do not decay immediately at the launching point of waves, even when the planet is as massive as Jupiter. Based on the results of hydrodynamic simulations, we also obtained an empirical model of wave propagation and damping for the cases of deep gaps. The one-dimensional gap model with our wave propagation model is able to well reproduce the gap structures in hydrodynamic simulations. In the case of a Jupiter-mass planet, we also found that the waves with smaller wavenumber (e.g., $m=2$) are excited and transport the angular momentum to the location far away from the planet. The wave with $m=2$ is closely related with a secondary wave launched by the site opposite from the planet.