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Astron. Astrophys. 343, 615-623 (1999)

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4. Conclusions

Our stability analysis has shown a flux tube model for quiescent prominences to be stable up to a critical width in the range of [FORMULA]. Increasing the central and external temperature and decreasing the height and the effective density contrast results in an increase of the critical width. The effective density contrast Eq. (18) contains the influence of the real density contrast, the external magnetic field and the external gas pressure. Decreasing the real density contrast and the external plasma beta stabilizes the prominence.

The critical widths we obtained are too small compared to observational data showing typical widths in the range of [FORMULA] to [FORMULA].

The periods of the oscillations for stable models are in good agreement with observed prominence oscillations.

The thin flux tube approximation represents an extreme of modeling solar prominences. Useful to describe fibril structures along the magnetic field lines it is an oversimplification when a whole prominence is to be described. Another extreme is the description with a continuous magnetic field, where the global stability analysis is more complicated than in the case of flux tubes. We found an external field to have a stabilizing effect on flux tube models. However, in contrast to a model with a continuous magnetic field, an interaction between the flux tube and the external plasma is not considered in the thin flux tube approximation. Thus it is interesting to compare our results with the stability of such a model. DeBruyne & Hood (1993) analysed the stability of the prominence model developed by Hood & Anzer (1990), which is the "continuous counterpart" of our flux tube model. They found stability for prominences with reasonable widths of [FORMULA] only below a height of about [FORMULA]. Using the parameters of their most stable models and taking into account that they adopted [FORMULA] inside the prominence and [FORMULA] in the corona, we obtain a critical width of only about [FORMULA] for a height of [FORMULA] in our models. This shows that the coupling of the whole field in a continuous model stabilizes the configuration. This can be understood intuitively on the basis of Fig. 11. The vertical displacement would cause a compression (on the left side) or a decompression (on the right side) of external field lines resulting in an increase or a decrease of the magnetic pressure, thus implying an additional restoring force, which stabilizes the configuration.

In Sect. 2 we showed that it is not possible to explain the observed prominence widths in terms of an equilibrium model which makes use of the thermal equilibrium described by Eq. (7). The stability analysis we presented here is based on equilibrium models which exclude the thermal equilibrium in order to be able to describe prominences with realistic widths by using temperature profiles with reasonable prominence properties. As the stability analysis is only dependent on the temperature profiles and not on the thermal equilibrium which is used to determine these profiles, our results give strong restrictions for the possible widths in flux tube models. There may exist thermal equilibria which allow for wider prominences. But if the widths exceed the critical values presented here, the dynamical stability gives the stronger restriction on the prominence width.

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999