New instruments such as the Diffraction Limited Spectro-Polarimeter (Sankarasubramanian et al. 2002; Lites et al. 2003) and the Polarimetric Littrow Spectrograph (Schmidt et al. 2003) have been designed to achieve significantly better resolutions in combination with adaptive optics systems. For the moment, however, no detailed observations of the penumbra near the diffraction limit have been carried out.

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The magnetic and kinematic properties of these two atmospheres vary with radial distance, as we will demonstrate in Sect. 5.

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... background

Another possibility is that there are vertical variations of the field structure that are sampled differently on the center and limb sides. We tend not to favor this explanation because it is not clear to us how differential opacity effects could produce a sharp discontinuity such as the observed one. Note that differential opacity effects should also influence one-component inversions. However, the one-component inversions of the same spot presented by Bellot Rubio (2003) do not feature discontinuities in the magnetic zenith angle.

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... densities

Densities are computed from gas pressures and temperatures using the ideal gas law. Gas pressures result from the condition ofhydrostatic equilibrium. Since we neglect magnetic forces in the equation of hydrostatic equilibrium, the densities (and therefore the Alfvén velocities) are only rough estimates.

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... penumbra

We systematically obtain slightly smaller flow speeds in the limb-side penumbra, perhaps as a consequence of differential opacity effects in a 3D structure with a Wilson depression.

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