The evolution of pitch angles of spiral arms

TL;DR

This paper examines how the pitch angles of spiral arms in galaxies evolve over time, comparing theoretical predictions with observational data to understand spiral structure formation.

Contribution

It provides an analysis of observed spiral arm pitch angles in relation to different formation theories, highlighting consistency with models predicting winding over time.

Findings

Observed pitch angles are broadly consistent with winding theories.

The distribution of cotangent of pitch angles supports the winding hypothesis.

Results align with expectations from theories involving spiral arm winding over time.

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.