The Characteristic Length Scale of the Magnetic Fluctuation in a Sunspot Penumbra: A Stochastic Polarized Radiative Transfer Approach

The characteristic size of penumbral structures are still below the current resolution limit of modern solar telescopes. Though we have seen a significant progress in theoretical work over the last decades no tight constraints can be placed on the size of penumbral structures in order to favor models with relatively large and thick magnetic flux elements, just at or below the current resolution limit, or on the other hand, clusters of optically thin micro-structures. Based on a macroscopic 2-component inversion and the approach of polarized radiative transfer in stochastic media, we have estimated the characteristic length scale of the magnetic fluctuation in a sunspot penumbra from observed Stokes spectra. The results yield a coherent picture for the entire magnetic neutral line of the penumbra and indicate that the magnetic fluctuations have a typical length scale between 30 km and 70 km.