Coronal magnetic field diagnostics via the Hanle effect of Lyman series lines

The magnetic field plays a major role in the physics of the solar corona. However, there are no direct measurements of this physical parameter. We describe a method that can provide the most direct determination of the vector magnetic field in the extended corona (i.e., at heliocentric heights between 1.2 R(solar radius) and 2.0 R(solar radius)). The method is based on polarimetric observations of UV lines of the Lyman series, that is, Lyman alpha (Ly-alpha), lambda 1216 A, Lyman beta (Ly-beta), lambda 1025 A, and Lyman gamma (Ly-gamma), lambda 972 A. These lines have a collisional and a resonantly scattered component. Linear polarization is induced in the resonant component by the anisotropy in the chromospheric radiation field that illuminates the corona. Magnetic fields can be suitably determined through the effects that they induce on this resonance polarization (Hanle effect). The Hanle effect of the Ly-alpha is sensitive to field strengths in the 10 - 100 gauss range. The resonance polarization of Ly-beta and Ly-gamma is sensitive, through the Hanle effect, to fields with strengths between 3 - 30 gauss, and 0.3 - 6 gauss, respectively. We describe a new method for separating the resonant from the collisional component of the Ly-beta and Ly-gamma; the method is based on the approximation, valid within 10%, that the collisional component of the Ly-alpha is negligible, in typical coronal conditions. From the intensity and the polarization of the resonant components of these Lyman lines, the strength and direction of coronal fields can be determined. We model the sensitivity of Hanle-effect diagnostics for different coronal structures (e.g., coronal holes and loops).