Stellar orbits and the persistence of spiral structure in galaxies.

The persistence of the spiral structure of galaxies is discussed in the context of the position probability of individual stars. The influence of the spiral-shaped perturbation to the axially symmetric background potential on this position probability is considered for the Galaxy in some special cases as a function of the assumed rotational velocity of the spiral pattern. It is found that for a given background and spiral potential, such a mechanism supporting the persistence of the spiral arms exists only in certain regions of rotational velocity of the spiral pattern.