Explaining persistent flat optical continua with moderate Balmer jumps in the decay phase

Explain the physical mechanism that produces persistent, flat optical continuum spectra in the red-optical during the gradual decay phase of M-dwarf flares while maintaining moderate Balmer jump ratios, reconciling observations with models such as optically thin Paschen continua and radiative backwarming that predict cooler temperatures and larger Balmer jumps than are observed.

Background

During the gradual decay phase, many flares show flat red-optical continua alongside moderate Balmer jump ratios. Existing explanations (optically thin Paschen continua or photospheric backwarming) predict cooler color temperatures and larger Balmer jumps than observed, leading to a noted "conundrum."

Resolving this discrepancy is crucial for accurately modeling flare energy partition and atmospheric response across wavelengths, and for interpreting broadband flare energetics (e.g., Kepler band contributions) in late phases.