Three-Dimensional Dust Stirring by a Giant Planet Embedded in a Protoplanetary Disk

The motion of solid particles embedded in gaseous protoplanetary disks is influenced by turbulent fluctuations. Consequently, the dynamics of moderately to weakly coupled solids can be distinctly different from the dynamics of the gas. Additionally, gravitational perturbations from an embedded planet can further impact the dynamics of solids. In this work, we investigate the combined effects of turbulent fluctuations and planetary dust stirring in a protoplanetary disk on three-dimensional dust morphology and on synthetic ALMA continuum observations. We carry out 3D radiative two-fluid (gas+1-mm-dust) hydrodynamic simulations in which we explicitly model the gravitational perturbation of a Jupiter-mass planet. We derived a new momentum-conserving turbulent diffusion model that introduces a turbulent pressure to the pressureless dust fluid to capture the turbulent transport of dust. The model implicitly captures the effects of orbital oscillations and reproduces the theoretically predicted vertical settling-diffusion equilibrium. We find a Jupiter-mass planet to produce distinct and large-scale three-dimensional flow structures in the mm-size dust, which vary strongly in space. We quantify these effects by locally measuring an effective vertical diffusivity (equivalent alpha) and find azimuthally averaged values in a range $\delta_\mathrm{eff}\sim5\cdot 10^{-3} - 2\cdot 10^{-2}$ and local peaks at values of up to $\delta_\mathrm{eff}\sim3\cdot 10^{-1}$. In synthetic ALMA continuum observations of inclined disks, we find effects of turbulent diffusion to be observable, especially at disk edges, and effects of planetary dust stirring in edge-on observations.