THE ELECTRICAL CURRENT DENSITY VECTOR IN THE INNER PENUMBRA OF A SUNSPOT

We determine the entire electrical current density vector in a geometrical three-dimensional volume of the inner penumbra of a sunspot from an inversion of spectropolarimetric data obtained with Hinode/SP. Significant currents are seen to wrap around the hotter, more elevated regions with lower and more horizontal magnetic fields that harbor strong upflows and radial outflows (the intraspines). The horizontal component of the current density vector is 3-4 times larger than the vertical; nearly all previous studies only obtain the vertical component J(z), thus strongly underestimating the current density. The current density (J) over right arrow and the magnetic field (B) over right arrow form an angle of about 20 degrees. The plasma beta at the 0 km level is larger than 1 in the intraspines and is one order of magnitude lower in the background component of the penumbra (spines). At the 200 km level, the plasma beta is below 0.3, nearly everywhere. The plasma beta surface as well as the surface optical depth unity is very corrugated. At the borders of intraspines and inside, (B) over right arrow is not force-free at deeper layers and nearly force-free at the top layers. The magnetic field of the spines is close to being potential everywhere. The dissipated ohmic energy is five orders of magnitudes smaller than the solar energy flux and thus negligible for the energy balance of the penumbra.