Radiative Mhd Simulation of Sunspot Structure

Results of a 3D MHD simulation of a sunspot with a photospheric size of about 20 Mm are presented. The simulation has been carried out with the MURaM code, which includes a realistic equation of state with partial ionization and radiative transfer along many ray directions. The simulation covers a time span of about 12 hours. The largely relaxed state of the sunspot shows a division in a central dark umbral region with bright dots and a penumbra showing bright filaments of about 3 to 4 Mm length with central dark lanes. By a process similar to the formation of umbral dots, the penumbral filaments result from magneto-convection in the form of upflow plumes, which become elongated by the presence of an inclined magnetic field: the upflow is deflected in the outward direction and bends down the magnetic field to become almost horizontal in the upper part of the plume near the level of optical depth unity. At the same time, roll-type motion leads to a flow perpendicular to the filament axis and to a downflow near its edges. Expansion and flux expulsion causes a strong reduction of the field strength in the upper part of the rising plume, where a dark lane forms owing to the piling up of matter near the cusp-shaped top and the upward bulging of the surfaces of constant optical depth. The simulated penumbral structure corresponds well to the observationally inferred interlocking-comb structure of the magnetic field with Evershed outflows along dark-laned filaments with nearly horizontal magnetic field and roll-type perpendicular motion, which are embedded in a background of stronger and less inclined field. Photospheric spectral lines are formed at the very top and somewhat above the upflow plumes, so that they do not fully sense the strong flow as well as the large field inclination and significant field strength reduction in the upper part of the plume structures. Subject headings: MHD – convection – radiative transfer – sunspots