Multiple pattern speeds in barred galaxies I. Two-dimensional models

We have studied the coexistence of several modes with different pattern spe eds in barred galaxies, by a simulation survey exploring a wide range of in itial conditions. The high resolution two-dimensional experiments cover the dynamical evolution for about one Hubble time. A remarkable feature of the se simulations is that in many cases the spiral structure is clearly visibl e in the stellar component for several gigayears and weakens so slowly that it can take more than 10 gigayears to become indiscernable even in the dir ect density plots. We confirm Sellwood and Sparke's (1988) results that the pattern speed of t he spiral arms may differ from that of the bar. However, we find several di fferent variations. There are systems where the bar and the spiral structur e are clearly corotating, whereas in others they have different pattern spe eds but are probably connected by a non-linear mode coupling as was suggest ed by Tagger et al. (1987). We have also found models with separate pattern speeds, but without evident mode coupling. Several simultaneous spiral mod es can also coexist in the disk, even overlapping in radius. Sometimes the systems have separate inner and outer spirals, the inner corotating with th e bar and the outer having a lower pattern speed. We conclude that similar variation can exist in real galaxies. Some morphol ogical features, like distinct spiral structures with large size difference s, can be best explained by separate coexisting patterns. However, there ar e cases where most of the disk is dominated by one mode. For example, galax ies with well developed outer rings are probably genuine examples of corota ting features. It is also possible that in the presence of two or more mode s, the appearance of the spiral structure changes considerably in a time sc ale of about one gigayear while the Hubble type of the galaxy stays the sam e.