Testing the Spiral Pitch Angle Against the Disc Shear Rate in the Milky Way

The angle at which spiral arms wind around the Galaxy and the rate at which the disc shears are not independent quantities, and the relation between them discriminates between arms that are material features, arms that are quasi-stationary density waves, and arms that are transient and recurrent. This paper assembles the test for the Milky Way from published local values. The Oort constants of the solar neighbourhood fix the local angular speed and the dimensionless shear. The published mean pitch angle of the Galactic arms then implies a definite radial spacing between arms at the solar circle for a two-armed pattern. Finally, treating the arms hypothetically as material features, the shear predicts how quickly the pitch would tighten, and the time to wind from a moderately open configuration to the observed one is computed explicitly. That winding time is far shorter than the age of the disc, so the observed pitch cannot be the long-lived state of material arms; the arms must be patterns, transient responses, or continuously regenerated. The paper quantifies each step so that improved pitch or shear measurements can be inserted directly.