3-D magnetic configurations supporting prominences: I. The natural presence of lateral feet

It is now commonly accepted that prominence plasma is supported in magnetic dips, in particular in twisted flux-tubes. But present two-dimensional models are unable to explain the observed presence and structure of prominences feet. This requires three-dimensional models. We modeled the field using linear force-free field equations. Combining a small number of harmonics, and using observational constraints, we have found the area in the parameter space where prominences are likely to be present. Then, adding 3-D harmonics, we show that feet appear periodically underneath the prominence body. For great helicity, the parameter space is mostly fulfilled by configurations which have feet alternating between both sides of the prominence axis, as observed. The theoretical photospheric field has a quasi-bipolar pattern and the prominence stands above a magnetic corridor containing only small parasitic polarities. The lateral feet are formed by dips in the vicinity of these small polarities. These configurations show in a natural fashion a number of well-established as well as more recent observationnal aspects of prominences, in particular the vector magnetic field measurements in prominences and the chirality patterns (the dextral/sinistral, right/left bearing, skew of the overlying coronal arcade and fibril organization in prominence channels).