Evidence For A Vertical Dependence on the Pressure Structure in AS 209.

We present an improved method to measure the rotation curves for disks with non-axisymmetric brightness profiles initially published in Teague et al. (2018a). Application of this method to the well studied AS$~$209 system shows substantial deviations from Keplerian rotation of up to $\pm 5\%$. These deviations are most likely due to perturbations in the gas pressure profile, including a perturbation located at $\approx 250~$au and spanning up to $\approx 50~$au which is only detected kinematically. Modelling the required temperature and density profiles required to recover the observed rotation curve we demonstrate that the rings observed in $\mu$m scattered light are coincident with the pressure maxima, and are radially offset from the rings observed in mm continuum emission. This suggests that if rings in the NIR are due to sub-$\mu$m grains trapped in pressure maxima that there is a vertical dependence on the radius of the pressure minima.