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Astron. Astrophys. 358, 665-670 (2000)

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6. Conclusions

The thermal/radiative stability of astrophysical gases under the influence of a distant source of radiation has been investigated in the grey approximation. The medium is found to be possibly unstable if it possesses a strongly temperature-dependent opacity with [FORMULA] in radiative equilibrium and if it is capable to achieve considerable optical depths by chemical processing. Both preconditions are fulfilled in dust forming gases. The proposed instability arises from (a) the extremely temperature-sensitive source of opacity in combination with (b) multidimensional radiative transfer effects.

Small initial fluctuations of the density and/or temperature structure in a dust forming medium will naturally result in likewise small fluctuations in the forming dust component. An emerging dust shell in the wind of a red giant is therefore not expected to be perfectly spherical symmetric at the time of its formation, but will already possess an internal, slightly patchy, spatial structure. The more opaque parts of this shell will block the outward directed radiation from the central star, while the radiative flux preferentially escapes through the in-between situated, optically thinner parts. Therefore, the more opaque parts will be accompanied by shadowed regions behind them. In these shadows, the temperature of the medium decreases faster than in the neighboring, more illuminated parts. Since the medium is close to the borderline where the temperature is just sufficiently low to become favorable for dust formation, a slight temperature decrease can strongly improve the conditions for subsequent dust formation and growth. Thus, the formation of dust will be accelerated in the shadowed, cooler regions and will be slowed down or even hindered in the illuminated, warmer regions, i.e. the spatial contrast of the degree of condensation will increase.

Such a physical system is self-amplifying, i.e. intrinsically unstable against various kinds of spatial perturbations of an initially homogeneous dust structure. The paper has considered in detail large-scale homogeneous perturbations of a spherically symmetric opacity structure taken from a stationary dust-driven wind model for a carbon star. Radial perturbation modes ([FORMULA]) are thereby found to be stable, whereas perpendicular perturbations ([FORMULA]) are found to be unstable in the outer parts of the dust formation / wind acceleration zone. This finding is consistent with the nature of the instability described above, which requires the formation of shadowed regions.

As a possible consequence of this instability, self-organization processes (also termed as structure or domain formation ) can be initiated in dust forming media, for example in the winds of red giants. The proposed instability is in particular expected to be involved in the formation of the irregular, cloudy dust structures observed around the infrared carbon star IRC+10216. According to the model, the characteristic time scale for the formation of such structures is determined by the speed of the dust formation process itself. The spatial extent of the emerging dust clouds is expected to correspond to an optical depth [FORMULA] at the time of their formation, which is a necessary precondition for the instability. Open questions remain especially when regarding possible interrelations with hydrodynamical processes. More detailed investigations are required here, which must combine time-dependent, hydrodynamical models of the dust formation process with radiative transfer calculations in more than one spatial dimension.

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© European Southern Observatory (ESO) 2000

Online publication: June 8, 2000