The evolution of pitch angles of spiral arms

Abstract

In spiral galaxies, the pitch angle, $\alpha$, of the spiral arms is often proposed as a discriminator between theories for the formation of the spiral structure. In Lin-Shu density wave theory, $\alpha$ stays constant in time, being simply a property of the underlying galaxy. In other theories (e.g tidal interaction, self-gravity) it is expected that the arms wind up in time, so that to a first approximation $\cot \alpha \propto t$. For these theories, it would be expected that a sample of galaxies observed at random times should show a uniform distribution of $\cot \alpha$. We show that a recent set of measurements of spiral pitch angles (Yu & Ho 2018) is broadly consistent with this expectation.