Circumstellar dust shells around long-period variables

Context. Long-period variables (LPVs) and Miras exhibit a pronounced variability in their luminosity with a more or less well-defined period, and they suffer large mass loss in the form of stellar winds. Owing to this extensive mass loss, they are surrounded by extended circumstellar dust shells (CDSs). The dynamics of these envelopes is the result of a complex interplay via an external excitation by the pulsating central star, dust formation, and radiative transfer. Aims. Our study is aimed at an understanding of the dynamics of CDSs around carbon-rich, standard luminous LPVs and Miras. These shells often show multiperiodicity with secondary periods as high as a few 104 d superimposed on a main period that is in the range of approximately 102−103 d. Such secondary periods may be caused at least in part by the presence of dust. Methods. We consider an excitation of the CDSs either by a harmonic force, provided by the oscillation of the central star, or by a stochastic force with a continuous power spectrum. The resulting numerically computed dynamical behaviour of the shell is analysed with the help of Fourier analysis and stroboscopic maps. Results. CDSs may be described as multioscillatory systems that are driven by the pulsating stars. A set of normal modes can be identified. The obtained periods of these modes are some 103 d, which is a characteristic timescale for dust nucleation, growth, and elemental enrichment in the dust formation zone. Depending on the oscillation period and strength of the central star, the envelope reacts periodically, multi- periodically, or irregularly.