Optically thin irregularities in the penumbrae of sunspots

Different estimates of the vertical gradient of magnetic field inclination in penumbrae disagree by 2 orders of magnitude. This disagreement may be resolved if measuring with typical angular resolutions implies averaging hundreds of independent fibrils whose residual variation, upon spatial averaging, gives rise to the observed large-scale structures. The small-scale gradients show up in estimates based on the broadband circular polarization, whereas significant bias affects other methods. From the comparison of these two types of measurements, one can infer the typical sizes of the penumbral irregularities. They turn out to be between 1 and 15 km wide, depending on details of the calculation. This result supports the kind of highly irregular atmosphere that Sanchez Almeida and coworkers proposed to represent the solar magnetic photosphere.