Thermal instability and non-equilibrium in solar coronal loops: from coronal rain to long-period intensity pulsations

The complex interaction of the magnetic field with matter is the key to some of the most puzzling observed phenomena at multiple scales across the universe, from tokamak plasma confinement experiments in the laboratory to the filamentary structure of the interstellar medium. \textbf{A major astrophysical puzzle} is the phenomenon of coronal heating, upon which the most external layer of the solar atmosphere, the corona, is sustained at multi-million degree temperatures on average. However, the corona also conceals a cooling problem. Indeed, recent observations indicate that, even more mysteriously, like snowflakes in the oven, the corona hosts large amounts of cool material termed coronal rain, hundreds of times colder and denser, that constitute the seed of the famous prominences. Numerical simulations have shown that this cold material does not stem from the inefficiency of coronal heating mechanisms, but results from the specific spatio-temporal properties of these. As such, a large fraction of coronal loops, the basic constituents of the solar corona, are suspected to be in a state of thermal non-equilibrium (TNE), characterised by heating (evaporation) and cooling (condensation) cycles whose telltale observational signatures are long-period intensity pulsations in hot lines and thermal instability-driven coronal rain in cool lines, \textbf{both} now ubiquitously observed. In this paper, we review this yet largely unexplored strong connection between the observed properties of hot and cool material in thermal non-equilibrium and instability and the underlying coronal heating mechanisms. \textbf{Focus is set on the long-observed coronal rain, for which significant research already exists, contrary to the recently discovered long-period intensity pulsations.} We further identify the outstanding open questions in what constitutes a new, rapidly growing field of solar physics.