Gas Response to Density Wave

Illustration using pendulums of the gas response to a density wave. For small amplitudes the response is linear, but for larger amplitudes it becomes non-linear. Above a certain threshold, the streamlines intersect (the pendulums collide) and there is a shock.

HI distribution in M81 shown as light on dark. HI iso-velocity contours are shown as solid lines, while the matching iso-velocity contours of the QSSS density wave theory are shown as symbol-lines. The QSSS theory does quite well at reproducing the velocity perturbations across the spiral arms.