Appendix A: The SSPSF model

The implementation of the stochastic self-propagating star formation (SSPSF) disk model is a variant of the prescriptions found in the reviews of Schulman & Seiden (1986) and, in more detail, Seiden & Schulman (1990). Major modifications are an exponentiated initial disk structure, a transition from a linearly increasing to a flat rotation curve, and the inclusion of spontaneous star formation. In particular, our model consists of 80 corotating rings, each with 6R cells, R being the ring number or radius. Thus we have a total of 18 960 cells. Initially, for each ring the number of occupied cells, N(r), has a probability proportional to a Gamma distribution $R~{\rm exp}(-R/R_{\rm d})$, with the scale length taken to be $R_{\rm d}=16$. On average the galaxies of our sample have a scale length of about 0.7 kpc, thus the linear size of each cell corresponds to about 44 pc. The polar angles for the N(r) cells in a ring are randomly chosen. At the start there are a total of 300 occupied cells. The life time of an occupied cell is 10 time steps, corresponding to about 10 Myr. The first time step following the activation of a cell, an empty neighbouring cell has a probability of 0.21 to become activated too. This implements the idea that the stellar wind of massive stars created in a cluster travels with a wind velocity of about 40 km s^-1 for about 1 Myr forming an increasingly dense shell that eventually fragments or hits other overdense regions, thus giving chance to the formation of new star-forming sites. At each time step, an additional 20 new cells are spontaneously activated; this sustains the number-density profile being exponential. Typically, an equilibrium occupation of around 1400 cells is reached after a few dozen time steps (providing a filling factor around 0.07), 10 percent of which having been just activated, and with the number density distribution remaining rather exponential out to about four scale lengths; further out there is a rapid drop or truncation of star-forming regions.

Either the rings rotate rigidly, with circular velocity being proportional to the ring radius, or differential rotation may be imposed by additionally demanding a constant circular velocity beyond a turnover radius $R_{\rm t}=2 R_{\rm d}$. For the simulations that included shear a flat rotation curve velocity of 500 km s^-1 was enforced, which is an unrealistic factor of $\sim$10 faster than observed for a typical dwarf irregular. However, this was only to clearly demonstrate the effect of strong shear within the model. As long as the circular velocity is much higher than the radial propagation velocity, shear seems to increase the star formation rate. For each simulated galaxy the number (and number density) distribution after 500 time steps was stored for use in the study of Sect. 4.4. The lump patterns and their corresponding distributions for a typical simulated galaxy can be seen in Fig. 9. Note that we simulate only the occurence of new and the presence of young stellar clusters, but otherwise assume a prevailing underlying population of older stars.