The structure and evolution of galacto-detonation waves - Some analytic results in sequential star formation models of spiral galaxies

Waves of star formation in a uniform, differentially rotating disk galaxy are treated analytically as a propagating detonation wave front. It is shown, that if single solitary waves could be excited, they would evolve asymptotically to one of two stable spiral forms, each of which rotates with a fixed pattern speed. Simple numerical solutions confirm these results. However, the pattern of waves that develop naturally from an initially localized disturbance is more complex and dies out within a few rotation periods. These results suggest a conclusive observational test for deciding whether sequential star formation is an important determinant of spiral structure in some class of galaxies.