2016ApJ...818...76J

We use extensive global two-dimensional hydrodynamic disk gas+dust simulations with embedded planets, coupled with three-dimensional radiative transfer calculations, to model the dust ring and gap structures in the HL Tau protoplanetary disk observed with the Atacama Large Millimeter/Submillimeter Array (ALMA). We include the self-gravity of disk gas and dust components and make reasonable choices of disk parameters, assuming an already settled dust distribution and no planet migration. We can obtain quite adequate fits to the observed dust emission using three planets with masses of 0.35, 0.17, and 0.26 M_Jup at 13.1, 33.0, and 68.6 AU, respectively. Implications for the planet formation as well as the limitations of this scenario are discussed.