Spectral lines for polarization measurements of the coronal magnetic field. II. Consistent treatment of the Stokes vector for magnetic-dipole transitions

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 differs from earlier treatments by Sahal-Brechot and House in the 1970s, in that the radiative emission coefficients for the four Stokes parameters, I, Q, U, and V, are treated to first order in a Taylor expansion of the line profile in terms of the Larmor frequency of the coronal magnetic field. In so doing, the influence on the scattered radiation of both atomic polarization, induced through anisotropic irradiation, and the Zeeman effect is accounted for in a consistent way. It is found that the well-known magnetograph formula, relating the V profile to the frequency derivative of the I profile, 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 field). 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.