Pitch Angle of Galactic Spiral Arms

TL;DR

This study investigates how the pitch angle of spiral arms in disk galaxies relates to the galactic rotation shear rate, using N-body simulations to reveal that the pitch angle depends on the shear rate and epicycle frequency, consistent with swing amplification theory.

Contribution

The paper provides a quantitative relation between spiral arm pitch angle and galactic shear rate through N-body simulations, explaining the dependence with swing amplification.

Findings

Pitch angle increases with epicycle frequency.

Pitch angle decreases with shear rate.

Derived a fitting formula for the relation.

Abstract

One of the key parameters that characterize spiral arms in disk galaxies is a pitch angle that measures the inclination of a spiral arm to the direction of galactic rotation. The pitch angle differs from galaxy to galaxy, which suggests that the rotation law of galactic disks determines it. In order to investigate the relation between the pitch angle of spiral arms and the shear rate of galactic differential rotation, we perform local $N$-body simulations of pure stellar disks. We find that the pitch angle increases with the epicycle frequency and decreases with the shear rate and obtain the fitting formula. This dependence is explained by the swing amplification mechanism.