Collapsed, uncollapsed, and hidden magnetic flux on the quiet Sun^⋆

¹ Institute of Astronomy, ETH Zurich, 8093 Zurich, Switzeland
e-mail: stenflo@astro.phys.ethz.ch
² Istituto Ricerche Solari Locarno, via Patocchi, 6605 Locarno Monti, Switzerland

Received: 6 December 2010
Accepted: 18 February 2011

Abstract

Since the first applications of the Stokes V line ratio in the early 1970s and the Hanle depolarization effect in the early 1980s we have had a dualistic view of quiet-Sun magnetism: intermittent kG flux tubes surrounded by an ocean of turbulent fields with strengths of order 10–100 G. There has been the concern that this dualism could be an artefact of using two mutually almost exclusive diagnostic tools, the Zeeman and Hanle effect. We find however that the Hinode line-ratio data alone, without any reference to the Hanle effect, reveal the existence of two distinct flux populations, representing strong (collapsed) and weak (uncollapsed) flux. The collapsed population is preferentially located in the intergranular lanes, while the uncollapsed population is most visible in the bright cell interiors. From a comparison between the intrinsic field strengths, as derived from the line ratio for the collapsed population, and the corresponding flux densities, we can deduce the size distribution of the flux tubes. The majority of them are found to have sizes in the range 10–70 km. The intrinsic flux tube field strength decreases with diminishing size to become substantially smaller than kG for sizes below about 60 km. Comparison between the average of the unsigned flux density in the Hinode quiet-Sun data set and earlier constraints from the Hanle depolarization effect shows that most of the flux remains invisible at the Hinode resolution scale due to cancellation of the opposite magnetic polarities within the spatial resolution element. We have derived the cancellation function that describes how the visibility of the hidden flux improves with increased spatial resolution. It needs to be extrapolated to extremely small scales before the constraints imposed by the Hanle effect get satified, which suggests that the bulk of the hidden flux resides at scales near the end of the magnetic scale spectrum (of order 10 m).