Spiral density wave theory, corotation resonance, and the velocity field of NGC 4321

We extend the exposition of a new kinematic method (exploiting geometric phase) for determining the corotation resonance radius of a grand-design spiral. We present an explicit formulation, in terms of first-order linear spiral density wave theory, for fitting to the velocity held of a grand-design spiral galaxy. We test the new formulation on the velocity field of the ionized gas in the grand-design spiral NGC 4321 in the Virgo Cluster using Fabry-Perot H alpha data. The kinematic method as currently implemented is useful specifically for determining an upper bound for the corotation resonance radius. We illustrate the kinematic evidence for the corotation resonance in the disk of NGC 4321.