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

TL;DR

This study reanalyzes Hinode quiet Sun spectropolarimetric data using Bayesian methods, revealing that magnetic field strengths are limited to upper bounds in the kG range and that the field inclination can be constrained only in high-signal pixels.

Contribution

It introduces a Bayesian inference approach with Markov Chain Monte Carlo to analyze solar magnetic fields, providing more detailed error estimates and constraints than previous methods.

Findings

Magnetic field strengths are constrained to upper limits, excluding kG regimes.

Noise significantly reduces information about magnetic field azimuth.

Some pixels with strong signals allow for constrained magnetic field inclination.

Abstract

Some recent investigations of spectropolarimetric observations of the Zeeman effect in the Fe I lines at 630 nm carried out with the Hinode solar space telescope have concluded that the strength of the magnetic field vector in the internetwork regions of the quiet Sun is in the hG regime and that its inclination is predominantly horizontal. We critically reconsider the analysis of such observations and carry out a complete Bayesian analysis with the aim of extracting as much information as possible from them, including error bars. We apply the recently developed BayesME code that carries out a complete Bayesian inference for Milne-Eddington atmospheres. The sampling of the posterior distribution function is obtained with a Markov Chain Monte Carlo scheme and the marginal distributions are analyzed in detail. The Kullback-Leibler divergence is used to study the extent to which the observations introduce new information in the inference process resulting in sufficiently constrained parameters. Our analysis clearly shows that only upper limits to the magnetic field strength can be inferred with fields in the kG regime completely discarded. Furthermore, the noise level present in the analyzed Hinode observations induces a substantial loss of information for constraining the azimuth of the magnetic field. Concerning the inclination of the field, we demonstrate that some information is available to constrain it for those pixels with the largest polarimetric signal. The results also point out that the field in pixels with small polarimetric signals can be nicely reproduced in terms of a quasi-isotropic distribution.