Physical origin of the FUV–U-band power-law scaling during flares

Explain and reproduce the observed power-law relationship between far-ultraviolet (FUV) continuum flux and U-band flux during stellar flares, identifying the physical processes and atmospheric layers responsible for the scaling and its rapid evolution relative to the U-band.

Background

High-resolution FUV studies report that FUV continuum variations scale as a power law with U-band flux, with slopes indicating faster FUV evolution than the U band in some events. Despite extensive modeling, the physical basis of this scaling remains unexplained.

Understanding this relationship would clarify the contributions of transition-region heating, chromospheric backwarming, and nonthermal processes to flare continuum emission across UV and optical bands.