Towards the measurement of coronal magnetic fields

Measurements of components of the vector magnetic field in the solar corona can potentially yield information critical to our understanding of coronal structure, dynamics and heating. I briefly review the magnetic information contained in forbidden coronal emission lines, which appear to have the highest potential to address some outstanding problems in coronal physics, especially those related to the storage and release of magnetic free energy. In practice, measurements of the full Stokes vector of lines of magnetic dipole (M1) character can only constrain both the line-of-sight field strength, B-parallel to, through the longitudinal Zeeman effect seen in Stokes V profiles, and the direction of the vector field projected onto the plane-of-the-sky, through the analysis of resonance scattering-induced linear polarization seen in Stokes Q and U, in the so-called "strong field" regime of the Hanle effect. Coupled with additional data and models, such polarimetry can reveal information on coronal magnetic fields, including current systems, unobtainable by other means available now or in the near future. In special cases where the "atomic alignment" is known and line-of-sight integration problems are unimportant, even the vector field can in principle be recovered. Stereoscopic measurements may ultimately provide a reliable way to invert data in the general case. I discuss the current challenges presented by such measurements, and mention some recent progress made in the development of the needed instrumentation.