Dust dynamics in planet-driven spirals

Context. Protoplanetary disks are known to host spiral features that are observed in scattered light, the ALMA continuum, and more recently in CO gas emission and gas dynamics. However, it is unknown whether spirals in gas and dust trace the same morphology. Aims. We aim to study the morphology and amplitude of dusty spirals as function of the Stokes number and the underlying mechanisms that cause a difference between dusty spirals and gas spirals. We then construct a model to relate the deviation from Keplerian rotation in the gas to a perturbation in surface density of the gas and dust. Methods. We used FARGO-3D with dust implementation to numerically study the spirals, after which the results were interpreted using a semi-analytical model. This model was tested on observational data to predict the perturbation of the spiral in gas dynamics based on the continuum data. Results. We find that the pitch angle of a spiral does not differ significantly between gas and dust. The amplitude of the dust spiral decreases with the Stokes number (St) and starts to fade out at a typical St > 0.1 as the dust becomes decoupled from the gas. The semi-analytical model provides an accurate and fast representation of the difference in the surface density of the spiral in dust and gas. We find a spiral in the TW Hya velocity residual map, never seen before, which is a feature in the vertical velocity and has a kink at the continuum gap, yielding strong evidence for a planet at 99 au. Conclusions. We built a model that gives an estimate of the underlying dynamics of dust in a spiral, which can serve as evidence of the planetary origin of spirals and can be a probe for the Stokes number in the disk.