A time dependent relation between EUV solar flare light-curves from lines with differing formation temperatures

Extreme ultraviolet (EUV) solar flare emissions evolve in time as the emitting plasma heats and then cools. Although accurately modeling this evolution has been historically difficult, especially for empirical relationships, it is important for understanding processes at the Sun, as well as for their influence on planetary atmospheres. With a goal to improve empirical flare models, a new simple empirical expression is derived to predict how cool emissions will evolve based on the evolution of a hotter emission. This technique is initially developed by studying 12 flares in detail observed by the EUV Variability Experiment (EVE) onboard the Solar Dynamics Observatory (SDO). Then, over 1100 flares observed by EVE are analyzed to validate these relationships. The Cargill and Enthalpy Based Thermal Evolution of Loops (EBTEL) flare cooling models are used to show that this empirical relationship implies the energy radiated by a population of hotter formed ions is approximately proportional to the energy exciting a population of cooler formed ions emitting when the peak formation temperatures of the two lines are up to 72% of each other and above 2 MK. These results have practical implications for improving flare irradiance empirical modeling and for identifying key emission lines for future monitoring of flares for space weather operations; and also provide insight into the cooling processes of flare plasma.