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