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Some recent investigations of spectropolarimetric observations of the Zeemaneffect in the Fe I lines at 630 nm carried out with the Hinode solar spacetelescope have concluded that the strength of the magnetic field vector in theinternetwork regions of the quiet Sun is in the hG regime and that itsinclination is predominantly horizontal. We critically reconsider the analysisof such observations and carry out a complete Bayesian analysis with the aim ofextracting as much information as possible from them, including error bars. Weapply the recently developed BayesME code that carries out a complete Bayesianinference for Milne-Eddington atmospheres. The sampling of the posteriordistribution function is obtained with a Markov Chain Monte Carlo scheme andthe marginal distributions are analyzed in detail. The Kullback-Leiblerdivergence is used to study the extent to which the observations introduce newinformation in the inference process resulting in sufficiently constrainedparameters. Our analysis clearly shows that only upper limits to the magneticfield strength can be inferred with fields in the kG regime completelydiscarded. Furthermore, the noise level present in the analyzed Hinodeobservations induces a substantial loss of information for constraining theazimuth of the magnetic field. Concerning the inclination of the field, wedemonstrate that some information is available to constrain it for those pixelswith the largest polarimetric signal. The results also point out that the fieldin pixels with small polarimetric signals can be nicely reproduced in terms ofa quasi-isotropic distribution.

Evidence for Quasi-isotropic Magnetic Fields from Hinode Quiet Sun Observations