Rossby-scaled saturation and multiple flare regimes in late type stars

ABSTRACT We investigate rotation–activity relations for white light flares in 147 Kepler late type stars, comprising more than 40 000 detected events. Flare equivalent durations are modelled with the OPEA formalism, yielding the Plateau, interpreted as the flare energy saturation level, and the Half-time, the time-scale required to approach this limit. Combining these parameters with rotation periods and Rossby numbers ($\mathrm{Ro}$), we test whether white light flare energetics follow the canonical dynamo saturation framework established from coronal diagnostics. Main-sequence stars separate into two statistically distinct flare regimes: although both follow similar scaling relations, they differ systematically in Half-time and Plateau. One main-sequence subset shows flare properties statistically indistinguishable from those of giants in several parameter planes, implying that flare regimes are not determined solely by evolutionary class. In the Plateau–$\mathrm{Ro}$ plane, main-sequence stars show clear two regime behaviour, with saturation thresholds at $\log \mathrm{Ro} \simeq -0.9$ and $-0.8$, consistent with canonical X-ray saturation thresholds. Giant stars instead follow a continuous scaling with no evidence of a saturation break. The Plateau increases towards cooler stars and follows a power law relation with Half-time, indicating that the upper envelope of white light flare energetics is governed not only by rotation, but also by convective depth and magnetic energy storage time-scales. Our results support $\mathrm{Ro}$ scaled saturation in white light flares and reveal multiple flare regimes within the main sequence.