# A Three-Dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk using DCO$^+$

## TL;DR

This study uses ALMA observations of molecular lines in the HD 163296 disk to place tight constraints on turbulence levels, revealing surprisingly low turbulence inconsistent with some theoretical models, and uncovers a complex chemical structure.

## Contribution

First direct multi-molecular line constraints on turbulence throughout the vertical disk structure, challenging existing turbulence theories and revealing detailed chemical ring features.

## Key findings

- Turbulence is constrained to be less than 0.06c_s, indicating very low turbulence levels.
- DCO$^+$ emission is confined to three concentric rings, showing complex chemical layering.
- Results challenge predictions of turbulence driven by magneto-rotational instability.

## 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_{\rm 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 $\alpha\lesssim$3$\times$10$^{-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$\pm$0.9 au, 149.9$^{+0.5}_{-0.7}$ au and 259$\pm$1 au, indicative of a complex chemical environment.