Nonlinear force-free modeling of magnetic fields in a solar filament

We present a striking filament pattern in the nonlinear force-free (NLFF) chromospheric magnetic field of the active region NOAA 10956. The NLFF chromospheric field is extrapolated from the Hinode high-resolution photospheric vector magnetogram using the weighted optimization method. The modeled structure is characterized by a highly sheared field with strong horizontal magnetic components and has a virtually identical shape and location as the filament seen in Hα. The modeled field strength agrees with the recent He i 10830Å observations by Kuckein et al.. The unequivocal resemblance between the NLFF extrapolation and the Hα observation not only demonstrates the ability of the NLFF field to reproduce chromospheric features, but also provides a valuable diagnostic tool for the filament magnetic fields.