Modal Approach to the Morphology of Spiral Galaxies. II. Dynamical Mechanisms

Abstract

A unified approach to spiral modes is carried out through the use of a cubic dispersion relationship developed earlier. This allows us to demonstrate the processes of maintenance and excitation of spiral modes of various morphologies separately for (a) normal spiral modes and (b) open spiral modes. In order to understand the relevant physical mechanisms and the general roles of the dynamical parameters (specified by the radial distribution of angular velocity, active surface density, and equivalent dispersive speed) the waves are described in terms of sustained wave trains. This allows us to examine the various dynamical issues discussed in Paper I. Very good accuracy is found when the present analytical results are compared with exact numerical data. The analytical approach makes it much easier to accomplish the process of identification of basic states from the observed spiral structure when a wide range of variation of the parameters of the basic state is involved. Our characterization of parameter regimes in terms of a few simple algebraic relations will be a useful guide for the construction of detailed quantitative models of specific galaxies and for general numerical surveys of classes of galaxies of given morphological types.