| Abstract
| - Aims. The magnetic field in the chromosphere of the quiet sun is too weak to be diagnosed via the general Zeeman effect. To obtain the hidden magnetic field vector, a complete comprehension of the linear polarization produced by scattering and modified by magnetic field is needed. We report a systematic and quantitative investigation of the sensitivity of the fractional linear polarization of the magnesium triplet to a weak magnetic field in the chromosphere, which can be a guide for the diagnostics of a weak magnetic field in the solar chromosphere. Methods. We focus on the fractional linear polarization of the magnesium triplet induced by scattering. We use the quantum theory under the flat-spectrum approximation developed by Landi Degl’Innocenti for the investigation. A seven-level atomic model of magnesium is adopted, while we do not take the radiative transfer or partial frequency redistribution (PRD) into account. Results. Polarization is directly related to the anisotropy factor, and modified by the continuum, collision, and magnetic field as well as dichroism effect. In our calculation, the elastic collision rates found are not large enough to destroy the population imbalances of the lower levels of the b2 and b1 lines. This is the prerequisite for the lower level Hanle effect and dichroism effect. When considering the dichroism effect, the magnetic field can influence the polarization not only in the line cores but also in the line wings. However, the magnetic field cannot obviously influence the polarization degree in the line wings once the continuum becomes significant. The polarization of the triplet is sensitive to the magnetic field between 0.001 and 0.1 Gauss due to the lower level Hanle effect and between 1 and 10 Gauss due to the upper level Hanle effect. In the lower level Hanle effect dominated region, the Q/ I amplitude of the b4 line increases with magnetic field strength because of the coupling among atomic alignments of the involved levels as described in the statistical equilibrium equations, while the amplitudes of the b2 and b1 lines decrease. In the upper level Hanle effect dominated region, the most sensitive line is the b4. Conclusions. The polarized lower levels and the contribution of dichroism have to be considered to fit the observed profiles of Mg I b triplet in the line cores. Therefore the b2 and b1 lines can be potential candidates for probing sub-Gauss range magnetic field, because their Q/ I amplitudes are sensitive to the magnetic field strength between 0.001 and 0.1 Gauss due to the lower level Hanle effect. The b4 line is suitable for diagnostics of magnetic field between 1 Gauss and 10 Gauss.
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