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

T NEUKIRCH*, M HESSE

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

We investigate the structure and stability of rotationally symmetric nonhomogeneous time-independent solutions derived from a simple analytic model of self-propagating star formation. For this purpose we employ two methodologies: We use bifurcation theoretical methods to prove the existence of nonhomogeneous axisymmetric stationary solutions of an appropriate nonlinear evolution equation for the stellar density. We show that the nonhomogeneous solution branch bifurcates from the homogeneous one at a critical parameter value of the star formation rate. Further, the analytical theory allows us to show that the new solution set 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 solutions. We conclude that no periodic time-dependent solutions of this special 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 provide a natural explanation, why long-lived large-scale structure have not been found in those simulations.

Original languageEnglish
Pages (from-to)840-847
Number of pages8
JournalAstrophysical Journal
Volume411
Issue number2
Publication statusPublished - 10 Jul 1993

Keywords

  • STARS, FORMATION
  • ERUPTIVE PROCESSES
  • DETONATION-WAVES
  • SPIRAL GALAXIES
  • EVOLUTION
  • PLASMAS
  • ONSET

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