A Three-dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk Using DCO⁺

Abstract

Gas kinematics are an important part of the planet formation process. Turbulence influences planetesimal growth and migration from the scale of sub-micron dust grains through gas-giant planets. Radio observations of resolved molecular line emission can directly measure this non-thermal motion and, taking advantage of the layered chemical structure of disks, different molecular lines can be combined to map the turbulence throughout the vertical extent of a protoplanetary disk. Here we present ALMA observations of three molecules (DCO + (3-2), C 18 O(2-1) and CO(2-1)) from the disk around HD 163296. We are able to place stringent upper limits (v turb <0.06c s , <0.05c s and <0.04c s for CO(2-1), C 18 O(2-1) and DCO + (3-2) respectively), corresponding to α 3×10 −3 , similar to our prior limit derived from CO(3-2). This indicates that there is little turbulence throughout the vertical extent of the disk, contrary to theoretical predictions based on the magneto-rotational instability and gravito-turbulence. In modeling the DCO + emission we also find that it is confined to three concentric rings at 65.7±0.9 au, 149.9 +0.5 −0.7 au and 259±1 au, indicative of a complex chemical environment.

New Constraints on Turbulence and Embedded Planet Mass in the HD 163296 Disk from Planet–Disk Hydrodynamic Simulations

“…The power index is same as I16, while the normalization is slightly different. Other studies (Rosenfeld et al 2013;Flaherty et al 2017) also suggest temperature profiles with power-law indices shallower than −0.5. We plot various mid-plane temperature profiles and corresponding disk aspect ratios in Figure 8.…”

“…This additional perspective is a supplement to previous efforts of turbulence measurement in the HD 163296 disk (e.g., Flaherty et al 2015Flaherty et al , 2017 and may help to understand the underlying physics. Our numerical model is described in Section 2.…”

“…Boneberg et al (2016) use CO observations to constrain the α of the order of 10 −3 within 90 au of the disk, which is in good agreement with our result. Flaherty et al (2015Flaherty et al ( , 2017 find that CO isotopes and DCO+ emissions 4 are consistent with gas turbulence velocity less than a few percent of the sound speed, corresponding to 10 3  a -. In particular, Flaherty et al (2017) suggest weak turbulence ( 3 10 3  a´-) in the outer disk (r>260 au), which seems to be contrary to our conclusion based on the planet-disk interaction model.…”

“…The hydro model stands for the isothermal temperature profile assumed in our hydrodynamic simulations, except two additional hydrodynamic simulations, ShallowT and LargeH 0 , presented in Section 3.4. We also plot mid-plane temperature profiles and disk aspect ratios from Rosenfeld et al (2013) and Flaherty et al (2017) in dashed lines labeled as R13 and F17, respectively.…”

“…Here, however, we try to understand the discrepancy of α-viscosity in the outer disk between our result and that in Flaherty et al (2017). One big assumption in Flaherty et al (2015Flaherty et al ( , 2017 is that the turbulent velocity dispersion is a constant fraction of the local sound speed throughout the disk, which may not be the case if MRI is operational. As a result, they are essentially deriving an intensity-weighted average value of α over the entire disk.…”