Parameterizing the Perturbed Rotational Velocities of Planet-induced Gaps

Recent submillimeter observations of ALMA reveal that many protoplanetary disks contain substructures like gaps or rings. The disk-planet interaction is believed to be the most likely gap formation scenario, and most previous numerical work attempted to constrain the planet mass using the density profiles of gas in the gaps. Since the dust and gas distributions likely differ from each other in protoplanetary disks, however, perturbed rotational velocities that directly probe the gas would give a more reliable estimate to the planet mass. In this work, we run two-dimensional hydrodynamic simulations to measure the amplitudes and widths of rotational velocity perturbations induced by planets with different mass. We present the parametric relations of the gap widths and depths as functions of the planet mass and disk properties. We also apply our relations to HD 163296 to infer the masses of embedded planets.