Wednesday, December 13, 2006 - 3:15pm
Johannes Schönke (Univ. Bremen):
"Hydrostatic Planetary Models from the Point of View of Dynamical Systems"
Abstract. We investigate a model of solid planetary cores embedded in a gaseous nebula within the framework of the nucleated instability hypothesis. All possible hydrostatic equilibrium states of a spherically symmetric core-envelope structure are considered. The envelope is said to consist of a self-gravitating ideal gas with a polytropic relation in addition and extends up to the Hill radius. Given initial conditions, like core mass, gas density and temperature at the core surface, the radial structure is uniquely determined. Of special interest are transformations of variables like mass and density into certain homology invariants, which change the respective system of differential equations into an autonomous one (i.e. a system which does not contain the independent variable, the radius in our case, explicitly). This gives us the opportunity to discuss the problem with methods developed in the theory of nonlinear, autonomous dynamical systems, giving us a deeper insight into general properties of the model. One result is an analytical interpretation of numerically computed planetary mass spectra, which have been done as a theoretical prediction, to be released before the next upcoming observational advances (e.g. CoRoT). In addition, we will present results of a linear stability analysis done for the model.