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Invisible Target Wmv 009

Unresolved fields are expected to produce cancellation of opposite-polarity Stokes V signals, as described in Sect. 2.3.1. We still do not know if this problem affects our measurements, but several indirect arguments suggest that some degree of Zeeman cancellation might be present in the observations. For example, the existence of mixed-polarity profiles (Sect. 4.2) already demonstrates that some pixels contain fields of opposite polarity (although in this case they are well recognizable in the Stokes V profiles and do not produce complete Zeeman cancellation). Also, the magnetic energy of IN fields inferred through Hanle diagnostics appears to be larger than that calculated from Zeeman measurements (e.g., Trujillo Bueno et al. 2004). This led to the concept of very small-scale, turbulent fields which would permeate the whole solar surface and would be invisible to Zeeman-sensitive lines because of complete cancellation of the correspondig Stokes V signals. Another argument is based on the abundance of asymmetric Stokes V profiles. Sánchez Almeida et al. (1996) argued that the existence of mixed-polarity magnetic fibrils with sizes of a few tens of km within the resolution element would be able to explain the large fraction of asymmetric profiles. Also possible is the operation of a local dynamo on the solar surface (Vögler and Schüssler 2007). In that case, the observed magnetic structures would be the result of the stretching of field lines by turbulent plasma motions, which would create a pattern of highly mixed-polarity fields prone to Zeeman cancellation.

Invisible Target wmv 009

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The existence of canopy fields appears to be supported by the analysis of Stenflo (2013), who finds a transition from preferentially vertical fields deep in the atmosphere to more horizontal fields above, based on the symmetry properties of Stokes Q and U. This suggests that there must be non-zero vertical gradients of the field inclination in the solar IN. The detection of such gradients would lend credence to the magnetic canopy scenario and therefore remains an important target for future investigations. As pointed out before, the first inversion of Hinode/SP data implementing gradients of the atmospheric parameters along the line of sight suggests that IN fields become more horizontal with height (Danilovic et al. 2016). It would be of great interest to know whether this result applies to individual structures as well or is valid only in a statistical sense.

Some authors have claimed a high degree of self-similarity in magnetograms taken at different spatial resolutions, concluding that the quiet Sun must consist of randomly oriented magnetic fields with sizes as small as 10 m (Stenflo and Holzreuter 2003). Self-similarity is a typical property of fractals. The fractal dimension of solar magnetic structures determined by Janßen et al. (2003) from 0\(.5^\prime \prime \) resolution magnetograms is \(D=1.2\), which also points to a self-similar organization of the field over a large range of scales. The extrapolation of this behavior to subresolution scales implies that every pixel contains the full distribution of magnetic fields. By further assuming that these fields have mixed polarities one arrives at the concept of turbulent fields invisible to the Zeeman effect (but detectable through the Hanle effect). However, it is not clear to what degree magnetoconvection should produce a perfect balance of mixed polarities on all spatial scales. This question must be addressed with future numerical simulations at much lower magnetic Prandtl numbers than are affordable nowadays (see discussion in Martínez Pillet 2013). The MISMA hypothesis also postulates the existence of optically thin magnetic irregularities with opposite polarities filling the resolution element, in agreement with a fractal structuring of the field. 350c69d7ab


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