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Solar filament are commonly thought to be supported in magnetic dips, inparticular, of magnetic flux ropes (FRs). In this Letter, from the observedphotospheric vector magnetogram, we implement a nonlinear force-free field(NLFFF) extrapolation of a coronal magnetic FR that supports a large-scaleintermediate filament between an active region and a weak polarity region. Thisresult is the first in that current NLFFF extrapolations with presence of FRsare limited to relatively small-scale filaments that are close to sunspots andalong main polarity inversion line (PIL) with strong transverse field andmagnetic shear, and the existence of a FR is usually predictable. In contrast,the present filament lies along the weak-field region (photospheric fieldstrength $\lesssim 100$ G), where the PIL is very fragmented due to smallparasitic polarities on both side of the PIL and the transverse field has a lowvalue of signal-to-noise ratio. Thus it represents a far more difficultchallenge to extrapolate a large-scale FR in such case. We demonstrate that ourCESE--MHD--NLFFF code is competent for the challenge. The numericallyreproduced magnetic dips of the extrapolated FR match observations of thefilament and its barbs very well, which supports strongly the FR-dip model forfilaments. The filament is stably sustained because the FR is weakly twistedand strongly confined by the overlying closed arcades.

Nonlinear Force-Free Field Extrapolation of a Coronal Magnetic Flux Rope Supporting a Large-Scale Filament from Photospheric Vector Magnetogram