Swing Amplification of Galactic Spiral Arms: Phase Synchronization of Stellar Epicycle Motion

Abstract

We revisit the swing amplification model of galactic spiral arms proposed by Toomre (1981). We describe the derivation of the perturbation equation in detail and investigate the amplification process of stellar spirals. We find that the elementary process of the swing amplification is the phase synchronization of the stellar epicycle motion. Regardless of the initial epicycle phase, the epicycle phases of stars in a spiral are synchronized during the amplification. Based on the phase synchronization, we explain the dependence of the pitch angle of spirals on the epicycle frequency. We find the most amplified spiral mode and calculate its pitch angle, wavelengths, and amplification factor, which are consistent with those obtained by the more rigorous model based on the Boltzmann equation by Julian and Toomre (1966).

31 pages, 11 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
• Short-term dynamical evolution of grand-design spirals in barred galaxies
• Pitch Angle of Galactic Spiral Arms
• Galactic Spiral Arms by Swing Amplification
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Cited by in corpus (9)

• The dynamics of stellar disks in live dark-matter halos
• Galaxy Zoo: constraining the origin of spiral arms
• Global N-Body Simulation of Galactic Spiral Arms
• Dynamics of Porous Dust Aggregates and Gravitational Instability of Their Disk
• Effect of finite disk-thickness on swing amplification of non-axisymmetric perturbations in a sheared galactic 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
• Signatures of simulated spiral arms on radial actions
• Linear Analysis of the Nonaxisymmetric Secular Gravitational Instability