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Astron. Astrophys. 342, 867-880 (1999)

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8. Conclusions

We have performed a detailed comparison of H[FORMULA] observations with the 3-D model for the magnetic configuration supporting quiescent filaments developed in Papers I and II. The model is based on the initial simple idea that filaments are formed by cold plasma trapped in magnetic dips. The main aim was to develop a model which could be compared precisely to observations and which could reproduce the feet of prominences, which have been a long-standing puzzle.

In the present paper we have extended the comparison to observations which we started in Paper II, using a series of SOHO/MDI line-of-sight magnetograms, as well as high resolution H[FORMULA] spectro-imaging data taken with the MSDP instrument on the German VTT (Tenerife). These observations were obtained during a coordinated campaign between space instruments aboard SOHO, Yohkoh and ground-based instruments, on September 25[FORMULA] 1996. In order to model the magnetic field in the observed filament channel, we used the linear magnetohydrostatic (lmhs ) extrapolation method developed by Low (1992). This method extends the usual linear force-free field (lfff ) extrapolation by including the effects of plasma pressure and gravity. The present study is the first attempt to use lmhs extrapolations in an observed filament channel. The inputs to the model are the observed photospheric longitudinal magnetic field (which was modeled by magnetic charges in Paper II), as well as a few parameters (see Table 2) which are estimated from the observations. The observed velocities of the photospheric magnetic polarities and of the plasma in the filament justify the present quasi-static approach used to study the filament evolution. The main hypotheses remain on the implicitly supposed distribution of the electric currents and the presence of a twisted flux-tube in the corona. These limitations are presently inherent not only in observations (in particular the absence of vector magnetograms), but also in the present modelling (due to difficulties to build 3-D non-linear models with observable boundary conditions).

Using the above assumptions (and keeping in mind the limitations given in Appendix B) the localization of the dips are in a surprisingly good agreement with the H[FORMULA] fine structures, both in the filament (body and feet) and in its channel (dark elongated fibrils). This finally justifies the chosen approach. The comparison of the model with H[FORMULA] observations is done through the computation of the field lines limited to their magnetic dips, filled up to a depth of 300 km (typical gravitational scale height of the plasma in filaments). In this way the lfff extrapolations give a fairly good localization of the filament body and feet. Including plasma pressure and gravity via lmhs extrapolations slightly improves the correlation with H[FORMULA] fine structures. It extends the distribution of dips and rotates the field direction towards the orientation of the observed H[FORMULA] fine structures. While we have forced the model to over-estimate the plasma effects up to the limit of physical validity, we still found that the plasma effects only lead to a relatively small deformation of the magnetic configuration. The locations of dips are mainly constrained by the magnetic shear and by the photospheric field distribution. It is also noteworthy that the exact distribution of the coronal electric currents is not of such a great importance (though it is more important than the plasma distribution) provided that a main twisted flux-tube is present together with the parasitic polarities.

In the filament channel H[FORMULA] dark features are usually present in the vicinity of low measured vertical magnetic fields at the limit of the instrumental noise of SOHO/MDI ([FORMULA] G). Nevertheless, some of the H[FORMULA] dark features can be correlated with low lying computed dipped field lines ([FORMULA] Mm). Consequently, despite of many of the theoretical and observational problems listed in Appendix B, the detailed comparison of the model with the observations can still be completed under such extreme conditions. This is in agreement with the results obtained by Aulanier et al. (1998b) on H[FORMULA] fibrils in an active region, with data from different instruments.

This series of papers brought further evidences of that twisted configurations are supporting at least some filaments in bipolar regions. The present model is a 3-D extension of previous twisted flux-tube models such as van Ballegooijen & Martens (1989), Démoulin & Priest (1989), Priest et al. (1989) and Low & Hundhausen (1995). The twisted flux-tube concept brings together, in a natural way, many of the so-long unrelated observations (see conclusion of Paper I). It explains the feet as a natural extension of the filament body, composed of a continuous dip pattern which joins the prominence body to the photosphere. These lateral dips form a natural extension of the central distribution of dips (in the prominence body), due to the presence of parasitic polarities in the filament channel. The shape and the evolution of the feet are linked to these observed parasitic polarities. The 3-D aspect of the model permits to make the link between the organization of the dips viewed from above (filaments) and from the side (filaments close to the limb and prominences).

Comparisons between filament/prominence models and observations bring new information on the highly non-potential magnetic configurations of the solar atmosphere. In a more general context, such investigations link the studies of the rise of magnetic flux-tubes through the convection zone to the CMEs in the corona and their associated interplanetary magnetic clouds. We hope that all the points emphasized in this paper will provide some insight so that observers and theoreticians can collaborate in order to apply relevant 3-D models of filaments/prominences through well oriented observing programs. In this context we hope to use the future observations from the French-Italian telescope THEMIS based at the Teide Observatory (Tenerife), which should provide simultaneous high cadence spectro-imagery and magnetic data.

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© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999
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