Galactic Spiral Arms by Swing Amplification

TL;DR

This paper investigates the formation and structure of stellar spiral arms in disk galaxies using the swing amplification model, deriving key parameters and validating results with N-body simulations, to understand how spiral features depend on galactic dynamics.

Contribution

It provides fitting formulae for spiral arm properties based on the swing amplification model and confirms these with N-body simulations, enhancing understanding of spiral arm formation.

Findings

Pitch angle and radial wavelength increase with epicycle frequency and Toomre's Q.

Amplification factor decreases rapidly with Q.

Number of spiral arms increases with shear rate.

Abstract

Based on the swing amplification model of Julian and Toomre (1966), we investigate the formation and structure of stellar spirals in disk galaxies. We calculate the pitch angle, wavelengths, and amplification factor of the most amplified mode. We also obtain the fitting formulae of these quantities as a function of the epicycle frequency and Toomre's $Q$. As the epicycle frequency increases, the pitch angle and radial wavelength increases, while the azimuthal wavelength decreases. The pitch angle and radial wavelength increases with $Q$, while the azimuthal wavelength weakly depends on $Q$. The amplification factor decreases with $Q$ rapidly. In order to confirm the swing amplification model, we perform local $N$-body simulations. The wavelengths and pitch angle by the swing amplification model are in good agreement with those by $N$-body simulations. The dependence of the amplification factor on the epicycle frequency in $N$-body simulations is generally consistent with that in the swing amplification model. Using these results, we estimate the number of spiral arms as a function of the shear rate. The number of spiral arms increases with the shear rate if the disk to halo mass ratio is fixed.