## 2. Conditions for fragmentation and molecularizationThe analysis of linear perturbations of transverse motions on a three-dimensional shell expanding into a uniform medium has been performed by Elmegreen (1994) and Vishniac (1994). Taking into account the convergence of the perturbed flow, stretching of the perturbed region due to expansion, and its own gravity, the instantaneous maximum growth rate of a transverse perturbation of a shell is given as where where is a dimensionless parameter. This maximum growth rate corresponds to the transversal angular wavenumber Another condition of the instability is that the wavelength of the
fastest transversal perturbation is within a
fraction of the shell, or smaller than which is equivalent to where . This is only a restriction to the
parameter if The fragmentation begins when both criteria are fulfilled for the first time, . We follow the expansion even beyond this time and evaluate the fragmentation integral : At the time when the fragments are well developed, so that clouds form at a later time. In the following sections, the models of an expanding shell are described, and the above instability criteria are tested. As soon as , the approximation of an expanding shell probably breaks down, and the fragments continue along individual galactic orbits. If the particle column density (where © European Southern Observatory (ESO) 1997 Online publication: March 24, 1998 |