Spiral structure and the dynamics of galaxies

A theory is proposed to explain the persistence of spiral structure in flat stellar systems. It is shown in a linear theory that spiral waves can grow spontaneously owing to star-wave interaction. The quasi-stationary spiral structure observed in actual galaxies is explained by the non-linear interaction of the growing stellar wave and the interstellar gas. It is shown that this interaction results in the time-asymptotic limit in a constant amplitude of the spiral wave. Finally we develop a quasi-linear theory of flat stellar systems that adequately can describe the properties of the stellar spiral waves on time-scales of the order of the life-time of these systems, provided the amplitude of the spiral wave does not become too large.