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Magneto-static models may overcome some of the issues facing force-freemagnetic field extrapolations. So far they have seen limited use and have facedproblems when applied to quiet-Sun data. Here we present a first application toan active region. We use solar vector magnetic field measurements gathered bythe IMaX polarimeter during the flight of the \sunrise{} balloon-borne solarobservatory in June 2013 as boundary condition for a magneto-static model ofthe higher solar atmosphere above an active region. The IMaX data are embeddedin active region vector magnetograms observed with SDO/HMI. This work continuesour magneto-static extrapolation approach, which has been applied earlier ({\itPaper I}) to a quiet Sun region observed with \sunrise{} I. In an active regionthe signal-to-noise-ratio in the measured Stokes parameters is considerablyhigher than in the quiet Sun and consequently the IMaX measurements of thehorizontal photospheric magnetic field allow us to specify the free parametersof the model in a special class of linear magneto-static equilibria. The highspatial resolution of IMaX (110-130 km, pixel size 40 km) enables us to modelthe non-force-free layer between the photosphere and the mid chromospherevertically by about 50 grid points. In our approach we can incorporate someaspects of the mixed beta layer of photosphere and chromosphere, e.g., taking afinite Lorentz force into account, which was not possible with lower resolutionphotospheric measurements in the past. The linear model does not, however,permit to model intrinsic nonlinear structures like strongly localized electriccurrents.

Magneto-static modelling from SUNRISE/IMaX: Application to an active region observed with SUNRISE II