Quiet Sun Magnetic Field Measurements Based on Lines with Hyperfine Structure

The Zeeman pattern of Mn I lines is sensitive to hyperfine structure (HFS) and, because of this reason, they respond to hG magnetic field strengths differently from the lines commonly used in solar magnetometry. This peculiarity has been employed to measure magnetic field strengths in quiet Sun regions. However, the methods applied so far assume the magnetic field to be constant in the resolution element. The assumption is clearly insufficient to describe the complex quiet Sun magnetic fields, biasing the results of the measurements. The diagnostic potential of Mn I lines can be fully exploited only after understanding the sense and the magnitude of such bias. We present the first syntheses of Mn I lines in realistic quiet Sun model atmospheres. Plasmas varying in magnetic field strength, magnetic field direction, and velocity, contribute to the synthetic polarization signals. The syntheses show how the Mn I lines weaken with increasing field strength. In particular, kG magnetic concentrations produce Mn I λ5538 circular polarization signals (Stokes V ) which can be up to two orders of magnitude smaller than what the weak magnetic field approximation predicts. As corollaries of this result, (1) the polarization emerging from an atmosphere having weak and strong fields is biased towards the weak fields, and (2) HFS features characteristic of weak fields show up even when the magnetic flux and energy are dominated by kG fields. For the HFS feature of Mn I λ5538 to disappear the filling factor of kG fields has to be larger than the filling factor of sub-kG fields. Since the Mn I lines are usually weak, Stokes V depends on magnetic field inclination according to the simple consine law, a scaling that holds independently of the magnetic field strength. Atmospheres with unresolved velocities produce very asymmetric line profiles, which cannot be reproduced by simple one-component model atmospheres. Inversion techniques incorporating complex magnetic atmospheres must be implemented for a proper diagnosis. Using the HFS constants available in the literature we reproduce the observed line profiles of nine lines with varied HFS patterns. Consequently, the uncertainty of the HFS constants do not seem to limit the use of Mn I lines for magnetometry. Subject headings: line: profiles – Sun: magnetic fields – Sun: photosphere