Appendix A: physical justification for the twisted flux-tube
The inclusion of an artificial background magnetic field creating a twisted flux-tube in the observed fields in the filament channel can be questioned. The main reason is that it modifies the observed magnetograms (e.g. see the difference between Fig. 1d and Fig. 1e). However, there are several arguments that justify this method.
(i) From Paper I: A systematic study of all the lfff configurations using the (;) diagrams for different values of has revealed that the OF twisted flux tube was the best configuration satisfying many different observational aspects of filaments and prominences, in particular the Hanle effect measurements of the magnetic field inside prominences, as well as underlying feet, lateral feet and chirality patterns of filaments. This "OF" terminology refers to an O-point at the center of the twisted flux tube and a flat field line at its bottom, with two X-points on the side (see Paper I).
(ii) From Paper II: OF twisted flux-tubes have been proven to be equivalent to OX flux-tubes perturbed by parasitic polarities in their vicinity, and the detailed study of the morphology of the lateral dipped structures associated with theoretical and observed parasitic polarities gave satisfactory results.
(iii) The presence of twisted configurations which support filaments could be a natural consequence of their build-up in the convection zone. Emonet & Moreno-Insertis (1998, and references therein) have shown that a minimum critical twist is needed so that a buoyant 2.5-D flux-tube is not destroyed during its rise by the hydrodynamic wakes which develop behind it. Moreover, for twists which are higher than the critical one, the combination of a higher buoyancy force in the central part of the flux-tube with the effect of the following wakes deform the magnetic configuration to the typical OF configuration. These results have been confirmed by Fan et al. (1998). The magnetic topology found in these MHD simulations is basically the same as the one found in lfff in Paper I which was there proven to be reliable for typical filaments. So far the MHD simulations studied the deep convection zone and not the emergence of the flux-tube through the photosphere, but it is very tempting to link these results. It is not yet fully clear how the dense plasma contained in the rising flux-tube is released through this emergence but it is thought to be a difficult and long process (see e.g. Low 1996), which is compatible with the long life of filament channels.
(iv) The prominence twisted flux-tube is also in agreement with the topology inferred from CMEs observed with the SOHO/LASCO coronagraph (e.g. Chen et al. 1997). In the interplanetary medium, twisted configurations are also identified in magnetic clouds (or interplanetary CMEs) with in situ measurements from Ulysses (e.g. Bothmer et al., 1996 and Weiss et al., 1996). The link between CMEs and prominence eruptions is highly probable both on a statistical ground (e.g. Bothmer & Schewnn 1994) and on deep study of individual cases (e.g. Burlaga et al., 1998).
(v) No twisted flux-tube can be found from direct lfff or lmhs extrapolations of the magnetograms. However, this is not inconsistent with the presence of such a flux-tube in the filament channel: a twisted flux-tube could be created by concentrated currents, which would not modify the vertical distribution of the magnetic field in the observed fields. Modelling such a magnetic configuration would require 3-D non-linear extrapolations in nlfff or nlmhs (e.g. Sakurai, 1989). Their effect would only be visible on the observed horizontal fields. Unfortunately, no measurements of the transverse fields are available for such low-field regions as filament channels, so that no observational constraint can be put on these currents. In this study we keep a "linear" approach (as in Papers I and II).
Appendix B: how can we explain the minor between differencesthe model and the observations?
In Sects. 4.2 and 6.2, we showed that the location, shape and orientation of most of the dark H absorbing features are correlated with the 3-D distribution of dipped field lines. However, some of these observed fine structures were poorly modeled by magnetic dips. We enumerate here all the reasons which we believe that may be the cause of these minor discrepancies, starting from the most probable ones and finishing with the less likely ones:
(i) Inhomogeneities of the shear distribution can be present. Their full treatment would require nlmhs extrapolations for which constant. Moreover, we cannot determine precisely the flux-tube parameters from the present observations. In order to do so, we would need transverse field measurements.
(ii) Some parasitic polarities observed by SOHO/MDI (see Fig. 1d) are very weak and may not always be reliable: their vertical field is below 10 G, which is very close to the instrumental noise of MDI (see Sect. 2.2 for details).
(iii) Every magnetic dips are not necessarily filled by dense and cold plasma, since this is determined by the energy balance of the plasma.
(iv) The function used is only a crude treatment of pressure and gravity in the filament channel. Other functions could be used, but a significant progress would require the description of the important density contrast between the prominence and the corona.
(v) The model does not take into account the effects of radiative transfer. In particular, the visibility of the fine structures is expected to be low where the density variations in the dips are not large compared to the chromospheric density.
(vii) The magnetic polarities have probably evolved between the observing time in H and the one of the magnetogram (see Table 1).
(viii) The periodicities of the model in the x and y directions introduce an artificial deformation of the configuration at the border of the computational box. In particular in the x direction, perpendicularly to the filament axis, the effect of the periodic boundary conditions in the main bipolar background photospheric field is to reduce the area in which field lines can connect these two opposite polarities (forming arcades overlaying the imposed twisted flux tube), compared to an extrapolation method which would not impose such periocities. Consequently the field line connectivity is poorly modeled in these regions for Mm, and the present method models the filament channel as if the observed inhomogeneous bipolar component was in fact less than 125 Mm wide, which is the period of the imposed boundary conditions.
(ix) Pressure-driven flows of dense plasma along flat field lines, can be observed in the H line center as horizontal flows. However, as this moving plasma is not located in magnetic dips, our representation cannot show it.
© European Southern Observatory (ESO) 1999
Online publication: February 23, 1999