Corotation resonance (${\Omega }_{\phi }={\Omega }_{\mathrm{p}}$)

A rotating gravitational pattern resonates with a stellar orbit when their azimuthal frequencies agree. In action-angle variables, this is the $k_R=0$ resonance of an azimuthal harmonic. Its torque changes azimuthal angular momentum without changing radial action to leading order, allowing stellar radial migration with little heating. The circular-orbit location is the corotation radius.