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Solar filaments are cold and dense materials situated in magnetic dips, whichshow distinct radiation characteristics compared to the surrounding coronalplasma. They are associated with coronal sheared and twisted magnetic fieldlines. However, the exact magnetic configuration supporting a filament materialis not easy to be ascertained because of the absence of routine observations ofthe magnetic field inside filaments. Since many filaments lie above weak-fieldregions, it is nearly impossible to extrapolate their coronal magneticstructures by applying the traditional methods to noisy photosphericmagnetograms, in particular the horizontal components. In this paper, weconstruct magnetic structures for some filaments with the regularizedBiot--Savart laws and calculate their magnetic twists. Moreover, we make aparameter survey for the flux ropes of the Titov-Demoulin-modified model toexplore the factors affecting the twist of a force-free magnetic flux rope. Itis found that the twist of a force-free flux rope is proportional to its axiallength to minor radius ratio, and is basically independent of the overlyingbackground magnetic field strength. Thus, we infer that long quiescentfilaments are likely to be supported by more twisted flux ropes than shortactive-region filaments, which is consistent with observations.

Magnetic Twists of Solar Filaments