Observability of the vertical shear instability in protoplanetary disk CO kinematics

<jats:p><jats:italic>Context.</jats:italic> Dynamical and turbulent motions of gas in a protoplanetary disk are crucial for their evolution and are thought to affect planet formation. Recent (sub-)millimeter observations show evidence of weak turbulence in the disk’s outer regions. However, the detailed physical mechanism of turbulence in these outer regions remains uncertain. The vertical shear instability (VSI) is a promising candidate mechanism to produce turbulence in the outer parts of the disk.</jats:p> <jats:p><jats:italic>Aims.</jats:italic> Our objective is to study the observability of the gas velocity structure produced by the VSI via CO kinematics with the Atacama Large Millimetre/submillimetre Array (ALMA).</jats:p> <jats:p><jats:italic>Methods.</jats:italic> We performed global 3D hydrodynamical simulations of an inviscid and locally isothermal VSI-unstable disk. We post-processed the simulation results with radiative transfer calculations and produced synthetic predictions of CO rotational emission lines. Next, we computed the line of sight velocity map and its deviations from a sub-Keplerian equilibrium solution. We explored the detectability of the VSI by identifying kinematic signatures using realistic simulated observations using the CASA package.</jats:p> <jats:p><jats:italic>Results.</jats:italic> Our 3D hydrodynamical simulations of the VSI show the steady state dynamics of the gas in great detail. From the velocity structure, we infer a turbulent stress value of <jats:italic>α</jats:italic><jats:sub><jats:italic>rϕ</jats:italic></jats:sub> = 1.4 × 10<jats:sup>−4</jats:sup>. On large scales, we observe clear velocity deviations of the order of 50 m s<jats:sup>−1</jats:sup> as axisymmetric rings with radially interspersed signs. By comparing synthetic observations at different inclinations we find optimal conditions at <jats:italic>i</jats:italic> ≲ 20° to trace for the kinematic structures of the VSI. We found that current diagnostics to constrain gas turbulence from nonthermal broadening of the molecular line emission are not applicable to anisotropic VSI turbulence.</jats:p> <jats:p><jats:italic>Conclusions.</jats:italic> We conclude that the detection of kinematic signatures produced by the VSI is possible with ALMA’s current capabilities. Observations including an extended antenna configuration are required to resolve the structure (beam sizes below ~10 au). The highest spectral resolution available is needed (~0.05 km s<jats:sup>−1</jats:sup> with ALMA Band 6) for a robust detection. The characterization of the large-scale velocity perturbations is required to constrain the turbulence level produced by the VSI from gas observations.</jats:p>