Multi-Scale Variability of Coronal Loops Set by Thermal Non-Equilibrium and Instability as a Probe for Coronal Heating

Solar coronal loops are the building blocks of the solar corona. These dynamic structures are shaped by the magnetic field that expands into the solar atmosphere. They can be observed in X-ray and extreme ultraviolet (EUV), revealing the high plasma temperature of the corona. However, the dissipation of magnetic energy to heat the plasma to millions of degrees and, more generally, the mechanisms setting the mass and energy circulation in the solar atmosphere are still a matter of debate. Furthermore, multi-dimensional modelling indicates that the very concept of a coronal loop as an individual entity and its identification in EUV images is ill-defined due to the expected stochasticity of the solar atmosphere with continuous magnetic connectivity changes combined with the optically thin nature of the solar corona. In this context, the recent discovery of ubiquitous long-period EUV pulsations, the observed coronal rain properties and their common link in between represent not only major observational constraints for coronal heating theories but also major theoretical puzzles. The mechanisms of thermal non-equilibrium (TNE) and thermal instability (TI) appear in concert to explain these multi-scale phenomena as evaporation-condensation cycles. Recent numerical efforts clearly illustrate the specific but large parameter space involved in the heating and cooling aspects, and the geometry of the loop affecting the onset and properties of such cycles. In this review we will present and discuss this new approach into inferring coronal heating properties and understanding the mass and energy cycle based on the multi-scale intensity variability and cooling properties set by the TNE-TI scenario. We further discuss the major numerical challenges posed by the existence of TNE cycles and coronal rain, and similar phenomena at much larger scales in the Universe.