Q-barrier and density spiral density wave formation in gaseous and stellar disks

The presence of a bulge in the center of a spiral galaxy makes it difficult to form a spiral pattern or a bar. This is especially true for galaxies with cusps, where the density is rapidly increasing when approaching the center. However, an unstable stellar disk model with a cusp is known in the literature. Using the methods of the linear theory of stability, formation a spiral pattern in a similar gaseous disk is considered. The role of the Q-barrier in the stellar and the gaseous disks is discussed.