Global Spiral Modes in NGC 1566: Observations and Theory

We present an observational and theoretical study of the spiral structure in galaxy NGC 1566. A digitized image of NGC 1566 in I band, obtained with the Australian National University 30 inch telescope, was used for measurements of the radial dependence of amplitude variations in the spiral arms. The azimuthal variations of the surface brightness in I band are about ±7% at 50'' radius and increase up to 57% at 100''. We use the known velocity dispersion in the disk of NGC 1566, together with its rotation curve, to construct linear and two-dimensional nonlinear simulations, which are then compared with observations. The linear stability analysis of the disk of NGC 1566, made under the assumption that the ratio of the vertical and the radial velocity dispersions is equal to 0.6, shows that the disk is stable with respect to spiral perturbations. We confirm this conclusion with two-dimensional hydrodynamical simulations. The disk of NGC 1566 is unstable if the ratio of the vertical and the radial velocity dispersions c_z/c_r is of order 0.8-1.0. Under this assumption, a two-armed spiral constitutes the most unstable global mode in the disk of NGC 1566. The two-dimensional hydrodynamic simulations of the unstable disk seeded with random perturbations show the exponential growth of two unstable modes, m = 2 and m = 3. The growth rates of the global modes seen in the nonlinear simulations are in good agreement with the results of the linear modal analysis. The m = 3 global mode is less important, however, in comparison with the main m = 2 global mode, and the overall evolution of the perturbations is determined by the two-armed spiral mode, which saturates at a level log₁₀ A₂ ≈ -0.5. The theoretical surface amplitude and the velocity residual variations across the spiral arms calculated during the nonlinear phase of instability are in qualitative agreement with the observations. The spiral arms found in the linear and nonlinear simulations are considerably shorter than those observed in the disk of NGC 1566. The nonlinear phase of instability is characterized by the transport of angular momentum toward the disk center, making the surface density distribution quite steep in comparison to the observations. We argue, therefore, that the surface density distribution in the disk of the galaxy NGC 1566 was different in the past, when spiral structure in NGC 1566 was growing linearly.