Spectral Lines for Polarization Measurements of the Coronal Magnetic Field. II. Consistent Treatment of the Stokes Vector for Magnetic‐Dipole Transitions

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Abstract
We present a compact, self-consistent formulation for the description of polarized radiation from magnetic-dipole transitions occurring in the magnetized solar corona. This work diÜers from earlier treatments by and House in the 1970s, in that the radiative emission coefficients for the Sahal-Breç chot four Stokes parameters, I, Q, U, and V , are treated to —rst order in a Taylor expansion of the line pro—le in terms of the Larmor frequency of the coronal magnetic —eld. In so doing, the in—uence on the scat- tered radiation of both atomic polarization, induced through anisotropic irradiation, and the Zeeman eÜect is accounted for in a consistent way. It is found that the well-known magnetograph formula, rela- ting the V pro—le to the frequency derivative of the I pro—le, must be corrected in the presence of atomic alignment produced by anisotropic irradiation. This correction is smallest for lines where collisions and cascades dominate over excitation by anisotropic radiation, but it systematically increases with height above the solar limb (up to a theoretical maximum of 100%, in the collisionless regime and in the limit of vanishing longitudinal magnetic —eld). Although the correction to the magnetograph formula must be calculated separately for each line as a function of heliocentric distance, it is likely to be small for some lines of practical interest, along lines of sight close to the solar limb. Subject headings: line: formationSun: atmosphereSun: coronaSun: magnetic —eld Over a century ago, eclipse data showed the presence in the solar corona of looplike structures reminiscent of magnetic- —eld patterns seen in the laboratory. Now we know that magnetic —elds emerging from solar subphotospheric layers, buÜeted by photospheric convective motions, control the dynamics and heating of the corona. However, in spite of enormous strides in our ability to determine vector magnetic —elds in the photosphere and properties of the plasma in the corona, our ability to determine properties of the coronal magnetic —elds remains severely limited. Away from strong —elds associated with active regions, few useful measurements of coronal —elds exist because they are extremely difficult to make. This is simply because the —elds in the quiet-Sun corona are intrinsically weak (D10 G) and their in—uence on the electromagnetic radiation emitted