MODAL APPROACH TO THE MORPHOLOGY OF SPIRAL GALAXIES .3. APPLICATION TO THE GALAXY M81

The modal approach to the morphology of spiral galaxies is applied to the galaxy NGC 3031 (M81) to demonstrate how the shape of the spiral pattern, specifically that obtained by Elmegreen et al. for the distribution of the stellar objects, may be used to help with the determination of the axisymmetric basic state of a galaxy with a reasonably regular spiral structure. The parameters of the basic state are narrowly constrained when all available observational data are taken into consideration, including both the mass distribution and the two components of velocity dispersion in the stellar disk. The ratio of the two components of velocity dispersion is found to be similar to that observed in the solar vicinity-a result that supports the reasonableness of the model. The mass distribution and the mass-to-light ratio obtained agree with that given by Kent from analysis of rotation curves. When compared with the work of Visser, it appears that he might have tended to use a heavier disk to support the gravitational field without including a sufficient amount of spherical components. The success of the present modeling process also supports the view that, to a first approximation, the spiral structure in many galaxies, essentially isolated at the present time, is a long-lasting, but in general slowly evolving, largely intrinsic characteristic of a galaxy. The possible influence of the companion NGC 3077 is discussed: the global spiral structure is approximately an intrinsic mode, but its exact nature is likely to be related to an earlier passage of this small companion.