Application of the global modal approach to spiral galaxies
  We have tested the applicability of the global modal approach in the density wave theory of spiral structure for a sample of six spiral galaxies: NGC 488, NGC 628, NGC 1566, NGC 2985, NGC 3938 and NGC 6503. The galaxies demonstrate a variety of spiral patterns from the regular open and tightly wound spiral patterns to a multi-armed spiral structure. Using the observed radial distributions of the stellar velocity dispersions and the rotation curves we have constructed equilibrium models for the galactic disks in each galaxy and analyzed the dynamics of the spiral perturbations using linear global modal analysis and nonlinear hydrodynamical simulations. The theory reproduces qualitatively the observed properties of the spiral arms in the galactic disks. Namely the theory predicts observed grand-design spiral structure in the galaxy NGC 1566, the tightly-wound spirals in galaxies NGC 488 and NGC 2985, the two-armed spiral pattern with the third spiral arm in the galaxy NGC 628, and the multi-armed spiral structure in the galaxies NGC 3938 and NGC 6503. In general, more massive disks are dominated by two-armed spiral modes. Disks with lower mass, and with lower velocity dispersion are simultaneously unstable for spiral modes with different numbers of arms, which results in a more complicated pattern. 
V. Korchagin (1,2), N. Orlova (2), N. Kikuchi (3), S.M. Miyama (4),   A.V. Moiseev (5) ((1) - Yale University, USA, (2) - In...