Circumstellar dust shells around long-period variables - IX. Dynamics of C-rich AGB star shells dominated by the exterior $kappa$-mechanism

摘要

Context. Miras and long-period variables (LPVs) are radially pulsating, highly evolved stars on the Asymptotic Giant Branch. Because of peculiar conditions of this objects, their cool, extended atmospheres are ideal sites for the formation of dust particles. Carbon-rich circumstellar dust shells (CDSs) surrounding stars with high stellar luminosity, tend to become dynamically unstable. They develop a self-maintaining oscillatory pattern caused entirely by dust formation even without the additional input of mechanical momentum from the star (exterior -mechanism). Since this system obviously has an eigenmode, it is interesting to consider the interaction with an exterior mechanical force, i.e. the radial pulsation at the inner boundary. Aims. We investigate in great detail the complex dynamical behaviour of carbon-rich CDSs in a more systematic way. This is done by established methods of nonlinear dynamics. Methods. We consider CDSs as multioscillatory systems that can be analysed with tools of nonlinear dynamics. We also use a discrete Fourier transform to examine the eigenmodes and their behaviour and apply this to a typical model CDS as a representative example. Results. In the absence of external excitation, the dynamics of the shell are dominated by its eigenmode, which is determined by the characteristic timescale of the coupled system of dust formation, hydrodynamics, and thermodynamics. The input mechanical energy and momentum of an underlying stellar pulsation introduces a new timescale to the system. Depending on the ratio of these two timescales, the dynamical behaviour of the system is either dominated by the eigenmode of the shell, by the excitation force, or can be irregular. In the latter case, the strength of the excitation becomes especially important. However, even for a small excitation period when the system is dominated by the shell's eigenmode, the oscillation of the shell tends to synchronise with the excitation force. Key words: chaos - hydrodynamics - methods: numerical - stars: AGB and post-AGB - stars: oscillations - stars: circumstellar matter