# Hydrodynamics and Dust Formation in the Circumstellar Shells of Miras and Long-Period Variables

A.J. Fleischer
Dissertation, Technische Universität Berlin, 1994
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### Abstract:

Miras and Long-period Variables (LPVs) are highly evolved stars on the Asymptotic Giant Branch. Due to the peculiar physical conditions of these luminous pulsating objects, their cool, extended atmospheres are distinguished sites for the formation of small solid particles (dust). A massive outflow or wind develops, which is driven by radiation pressure on dust. Dust particles influence both, the internal structure of the circumstellar shell as well as the optical appearance of Miras and LPVs. A thorough description of the circumstellar dust shells (CDS) around Miras and LPVs is necessary for a comprehensive understanding of this important stage of the cosmic cycle of matter.

The CDS around Miras and LPVs have to be considered as complex nonlinear systems, which require a consistent treatment of hydrodynamics, dust formation, thermodynamics, and chemistry to achieve a reliable model description. Hence, dynamical models of CDS around carbon-rich Miras and LPVs are presented, which include, consistently coupled, time-dependent hydrodynamics and a detailed treatment of the processes of formation, growth and evaporation of dust grains as well as radiative transfer and a treatment of the chemistry of the gas phase.

The results stress the necessity of taking into account the relevant physical interactions. Thereby, the dust complex is revealed as the decisive component which dominates the dynamics of the CDS. Radiation pressure on dust, supported by the interior pulsation, is shown to drive the wind, but moreover, the dust complex is able to induce its own strong shock waves which travel through the atmosphere and predominate the circumstellar structure. Furthermore, due to this mechanism of dust-induced shocks, the radial structure of the CDS appears to have a discrete or onion-shell like structure, which also results in an inhomogeneously distribution of the dust grains.

The abundance ratio of carbon to oxygen turns out to be a key parameter for the model calculations. For sufficiently high values of the carbon overabundance the time scale of the CDS behaves in accordance with the time scale of the interior pulsation. However, if the overabundance of carbon is reduced the CDS develops a separate time scale, multiple times longer than the pulsational time scale, an effect which we call multiperiodicity. Furthermore, an increase of the abundance of carbon to oxygen results in an increased outflow velocity. As a result of this linear correlation the derivation of carbon overabundances from the measurement of final outflow velocities becomes, in principle, possible. A direct derivation of the photospheric overabundance from observations is a difficult task, which has been possible only for a rather limited number of objects.

For sufficiently luminous models an instability occurs. In this work this new effect is called exterior $\kappa$-mechanism since the dust opacity plays the key role. In these models, radiation pressure on dust induces strong shocks, even in the absence of an interior pulsation. The absorption of stellar radiation by the dust particles causes an acceleration of the material, and moreover, the generation of small amplitude waves in the inner dustfree region, due to the backwarming of the dust. In turn, these waves trigger dust formation and impose a time scale on the dynamical system, and thus they close the cyclic self-maintaining process.

Dust-induced shocks as well as multiperiodicity are shown to influence decisively the optical appearance of the dust shell models by effects, which, in principle, are also present in observations of the objects under consideration.