Galactic Spiral Arms by Swing Amplification

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.

23 pages, 10 figures, accepted for publication in ApJ

References in corpus (6)

• Dawes Review 4: Spiral Structures in Disc Galaxies
• The origin of large peculiar motions of star-forming regions and spiral structures of our Galaxy
• Constraining dark matter halo profiles and galaxy formation models using spiral arm morphology. I. Method outline
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• Global N-Body Simulation of Galactic Spiral Arms
• Swing Amplification of Galactic Spiral Arms: Phase Synchronization of Stellar Epicycle Motion
• Planetesimal Formation by Gravitational Instability of a Porous-Dust Disk
• Effect of finite disk-thickness on swing amplification of non-axisymmetric perturbations in a sheared galactic disk
• Dynamics of Porous Dust Aggregates and Gravitational Instability of Their Disk
• Coherent Stellar Motion in Galactic Spiral Arms by Swing Amplification
• Elementary Process of Galactic Spiral Arm Formation: Phase Synchronization of Epicyclic Motion by Gravitational Scattering
• Extragalactic magnetism with SOFIA (SALSA Legacy Program) -- IV: Program overview and first results on the polarization fraction