BIFURCATION-ANALYSIS OF A SIMPLE ANALYTIC MODEL OF SELF-PROPAGATING STAR-FORMATION

We investigate the structure and stability of rotationally symmetric n onhomogeneous time-independent solutions derived from a simple analyti c model of self-propagating star formation. For this purpose we employ two methodologies: We use bifurcation theoretical methods to prove th e existence of nonhomogeneous axisymmetric stationary solutions of an appropriate nonlinear evolution equation for the stellar density. We s how that the nonhomogeneous solution branch bifurcates from the homoge neous one at a critical parameter value of the star formation rate. Fu rther, the analytical theory allows us to show that the new solution s et is stable in the weakly nonlinear regime near the bifurcation point . To follow the solution branch further, we use numerical methods. The numerical calculation shows the structure and stability of these solu tions. We conclude that no periodic time-dependent solutions of this s pecial model exist, and no further bifurcations can be found. The same results have been found in simulations of stochastic self-propagating star formation based on similar models. Therefore, our findings provi de a natural explanation, why long-lived large-scale structure have no t been found in those simulations.