Circumstellar Dust Shells of pulsating Red Giants as Dynamical Systems

S. Meier, A.B.C. Patzer, M. Lüttke, P. Woitke and E. Sedlmayr

Astronomische Gesellschaft Abstract Series, Vol. 17., (2000)

Abstract:

Miras and long-period variables (LPVs) are highly evolved, pulsating stars on the Asymptotic Giant Branch (AGB) with massive outflows and prominent circumstellar dust shells (CDSs). A CDS, driven by the stellar pulsation, can be considered as a dynamical system which reveals various kinds of complex phenomena like spatio-temporal instabilities, bifurcations, multiperiodicity and transition to chaos.

In order to analyze the temporal behavior of the CDS standard methods known from the theory of non-linear dynamical systems are applied. We have developed a spherical symmetric, multi-zone description for the CDS which includes the important physical interactions by means of non-linear coupling terms. The corresponding Hamiltonians are derived.

We present Poincaré maps for several models with a different number of zones in order to characterize their dynamical stability. The role of pulsation and dust formation for the development of the dynamical structure of the CDS is investigated. In addition, the linearized approximation of an one-zone model is discussed with respect to the Kolmogorov-Arnold-Moser and the Poincaré-Birkhoff theorems.

Keywords:

Hydrodynamics: dynamical system -- Stars: LPV -- Stars: mass-loss