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

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