Polarimetry of cool atmospheres: From the Sun to exoplanets

This is a review of a decade-long effort to develop novel tools for exploring magnetism in cold astrophysical media and to establish a new field of molecular spectropolarimetry since Berdyugina et al. (2000). It is most directly applicable to the Sun, cool stars, substellar objects, planets and other minor bodies as well as interstellar and circumstellar matter. It is close to being a mature field with developed theoretical tools poised to uncover new insights into the magnetic structures in cooler environments. Here I attempt a broad description of the literature and present some recent exciting results. In particular, following my programmatic review at Solar Polarization Workshop 3, I discuss advances in molecular magnetic diagnostics which are based on the modeling of about a dozen diatomic molecules with various electronic transitions and states, including the most challenging - FeH. The applications stretch from sunspots to starspots, small-scale and turbulent solar magnetic fields, red and white dwarfs, and spin-offs such as polarimetry of protoplanetary disks and exoplanets.