The vertical structure and kinematics of grand design spirals

We use an N-body simulation to study the 3D density distribution of spirals and the resulting stellar vertical velocities. Relative to the disc's rotation, the phase of the spiral's peak density away from the mid-plane trails that at the mid-plane. In addition, at fixed radius the density distribution is azimuthally skewed, having a shallower slope on the trailing side inside corotation and switching to shallower on the leading side beyond corotation. The spirals induce non-zero average vertical velocities, < V-z >, as large as < V-z > similar to 10-20 km s(-1), consistent with recent observations in the Milky Way. The vertical motions are compressive (towards the mid-plane) as stars enter the spiral, and expanding (away from the mid-plane) as they leave it. Since stars enter the spiral on the leading side outside corotation and on the trailing side within corotation, the relative phase of the expanding and compressive motions switches sides at corotation. Moreover, because stars always enter the spiral on the shallow density gradient side and exit on the steeper side, the expanding motions are larger than the compressing motions.