New constraints on turbulence and embedded planet mass in the HD 163296 disk from planet-disk hydrodynamic simulations

Abstract

Recent Atacama Large Millimeter and Submillimeter Array (ALMA) observations of the protoplanetary disk around the Herbig Ae star HD 163296 revealed three depleted dust gaps at 60, 100 and 160 au in the 1.3 mm continuum as well as CO depletion in the middle and outer dust gaps. However, no CO depletion was found in the inner dust gap. To examine the planet--disk interaction model, we present results of two-dimensional two fluid (gas + dust) hydrodynamic simulations coupled with three-dimensional radiative transfer simulations. In order to fit the high gas-to-dust ratio of the first gap, we find the Shakura--Sunyaev viscosity parameter $\alpha$ must be very small ($\lesssim 10^{-4}$) in the inner disk. On the other hand, a relatively large $\alpha$ ($\sim 7.5\times 10^{-3}$) is required to reproduce the dust surface density in the outer disk. We interpret the variation of $\alpha$ as an indicator of the transition from an inner dead zone to the outer magnetorotational instability (MRI) active zone. Within $\sim 100$ au, the HD 163296 disk's ionization level is low, and non-ideal magnetohydrodynamic (MHD) effects could suppress the MRI, so the disk can be largely laminar. The disk's ionization level gradually increases toward larger radii, and the outermost disk ($r > 300$ au) becomes turbulent due to MRI. Under this condition, we find that the observed dust continuum and CO gas line emissions can be reasonably fit by three half-Jovian-mass planets (0.46, 0.46 and 0.58 $M_\textrm{J}$) at 59, 105 and 160 au, respectively.