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Fine structure, magnetic field and heating of sunspot penumbrae

We interpret penumbral filaments as due to convection in field-free, radially aligned gaps just below the visible surface of the penumbra, intruding into a nearly potential field above. This solves the classical discrepancy between the large heat flux and the low vertical velocities observed in the penumbra. The presence of the gaps causes strong small-scale fluctuations in inclination, azimuth angle and field strength, but without strong forces acting on the gas. The field is nearly horizontal in a region around the cusp-shaped top of the gap, thereby providing an environment for Evershed flows. We identify this region with the recently discovered dark penumbral cores. Its darkness has the same cause as the dark lanes in umbral light-bridges, reproduced in numerical simulations by Nordlund and Stein (2005). We predict that the large vertical and horizontal gradients of the magnetic field inclination and azimuth in the potential field model will produce the net circular polarization seen in observations. The model also explains the significant elevation of bright filaments above their surroundings. It predicts that dark areas in the penumbra are of two different kinds: dark filament cores containing the most inclined (horizontal) fields, and regions between bright filaments, containing the least inclined field lines.