Prominences are thin structures consisting of cold plasma embedded in the hot corona. Their global shape has been known since a long time (e.g. d'Azambuja & d'Azambuja 1948). Prominences consist of bridges of chromospheric-like material located in the corona. Periodically the prominence connects to the photosphere by, so called feet or barbs, similar to road bridges. In this paper we use the term "feet", rather than "barbs", because in the model that we describe the dense material is supported while the term "barbs" was used by Martin et al. (1994) in the context of absence of dips, i.e. magnetic support. (More specific observations of the prominence morphology are introduced below in comparison with the model.)
Prominences are always found above inversion lines of the photospheric magnetic field in regions, called corridors or filament channels, which are nearly free of chromospheric fibrils (Martres et al. 1966). They are also characterized on either side by the presence of H fibrils nearly aligned with the inversion line, indicating a high magnetic shear (Foukal 1971; Rompolt 1990). The corridor is nearly free of vertical magnetic field flux except of small parasitic polarities (Martin 1990). A necessary condition for prominence formation is a low gradient transverse to the photospheric inversion line, of the vertical field component (Shelke & Pande 1983; Maksimov & Ermakova 1985; Maksimov & Prokopiev 1995).
In prominences the Zeeman effect only allows the measurement of the longitudinal component of the magnetic field (see Kim 1990 and references therein). The Hanle effect gives the three components of the field (and the electron density) from the polarization measurements in two spectral lines (e.g. Bommier et al. 1994). The compatibility of the results obtained by these two independent methods and by different groups of observers has strongly contributed to validate their respective results (see the reviews of Leroy 1988, 1989 and Kim 1990). It is now well accepted that the magnetic field in prominences is nearly horizontal (since Athay et al. 1983), while compatible with a slight dip configuration (Bommier et al. 1986, 1994). The magnetic field strength is nearly homogeneous (Leroy 1989) at the scale of few arc seconds, but show a statistical increase of strength with height which is compatible with a dip configuration (e.g. Leroy et al. 1983). One main result of Hanle measurements is that the prominence field has the opposite direction to the one expected from extrapolation of photospheric measurements (e.g. Leroy et al. 1983). Not only the field component orthogonal to the prominence is opposite to the field of a simple arcade (referred as an Inverse configuration), but also the field component parallel to the prominence is opposite to those of an arcade that would have been sheared by differential rotation ! A large majority of prominences are in the Inverse type (75% in Leroy et al. 1984, 85% in Bommier et al. 1994 and greater than 90% in Bommier & Leroy 1997).
Because the plasma is low in the corona as in prominences, the magnetic field plays a key role in all the processes involved. It channels both the plasma motions and the thermal conduction. It allows support against gravity of the prominence plasma one hundred times denser than the coronal plasma. In the present paper we will emphasize the importance of this last point and show that the necessity of magnetic support (in magnetic dips) naturally implies the observed 3-D shape of prominences, in particular the presence of lateral feet.
The gravitational scale height of prominence material is much lower than the typical height of prominences. This implies that gas pressure cannot be the mechanism of support. The observed velocities (few km s-1) are much less important than the free-fall velocities (several 10 km s-1) and usually, the velocity maps do not show a pattern similar to the one seen in arch filament systems (Schmieder 1989). Then the cold prominence plasma should be supported by the magnetic field. If enough mass (i.e. a plasma beta greater than 0.05) can be brought at the top of sheared magnetic arcade in less than one hour, the gravity force can bend down at the top of the arcade, providing a stable support to the prominence plasma (Schmieder et al. 1991; Fiedler & Hood 1993). However prominence formation takes usually a few days (resp. few weeks) for prominences in (resp. outside) active regions (e.g. Malherbe 1989). It implies that a magnetic dip should be present in the magnetic configuration before any dense material can slowly accumulate there.
The need of a magnetic dip for stable support was first pointed out by Kippenhahn & Schlüter (1957), however, the implications of such a condition were used only recently to select magnetic configurations suitable for prominence formation (see Priest et al. 1989 for developments). Apart from quadrupolar regions, where a dip is naturally present between the two bipoles, usually a dip is not present in a simply connected bipolar region. For instance, Amari et al. (1991) have proved that, in a bipolar region, a 2.5-D force-free field with an arcade topology cannot have a dip. This is however possible in 3-D with a overlying arcade compressing locally the central-part of an underlying sheared arcade (Antiochos et al. 1994). Another way to create a dip is to form a twisted configuration (e.g. in a 2.5-D linear force-free field, Démoulin & Priest 1989). Twisted configurations can be formed in several ways: by photospheric twisting motions (Priest et al. 1989), by converging motions in a sheared arcade with magnetic reconnection at the inversion line (van Ballegooijen & Martens 1989; Choe & Lee 1992), by resistive instability in an sheared arcade (e.g. Inhester et al. 1992), by relaxation and accumulation of helicity (e.g. Rust & Kumar 1994) or by emergence with inherent twist from the convective zone (e.g. Low 1994).
Twisted configurations are promising magnetic configurations for prominences, in particular because dense material can be naturally supported in them and because there are observationnal evidences of them (mainly in prominence eruptions, e.g. Raadu et al. 1988; Vrnak et al. 1991). Our aim in this paper is to go further than this usual statement by showing that 3-D twisted configurations permit to interpret a variety of observations within a single magnetic configuration. After a summary of the method in Sect. 2, we first analyze configurations invariant by translation in Sect. 3 with the aim to classify the variety of possible topologies in the parameters space. We then analyze examples of 3-D magnetic configurations in the Sect. 4 and show that the simple dip constraint leads naturally to the formation of prominence feet. Finally, in Sect. 5, we confront the properties of our model magnetic configurations with a variety of observed features of prominences.
© European Southern Observatory (ESO) 1998
Online publication: December 16, 1997