2025A&A...699A..90B

In the study of stellar flares, traditional method of calculating total energy emitted in the continuum assumes the emission originating from a narrow chromospheric condensation region with a constant temperature of 10 000 K and variable flare area. However, based on multicolor data from seven new flares observed in Białków and Shumen observatory and eight previously published flares observed on ten main-sequence stars (spectral types M5.5V to K5V - nine M-dwarfs and one K-dwarf) we show that flare areas had a relative change in the range of 10-61% (for more than half of the flares this value did not exceed 30%) throughout the events except for the impulsive phase, and had values starting from 50 ± 30 ppm to 300 ± 150 ppm for our new flares and from 380 ± 200 ppm to 7600 ± 3000 ppm from previously published flare data, while their temperature increased on average by the factor 2.5. The peak flare temperatures for our seven observed flares ranged from 5700 ± 450 K to 17 500 ± 10 050 K. Five of these flares had their temperatures estimated using the Johnson-Kron-Cousins B filter alongside TESS (Transiting Exoplanet Survey Satellite) data, one flare was analyzed using the SLOAN g' and r' bandpasses, and another was evaluated using both the SLOAN g' and r' bandpasses and TESS data. Using flare temperature and area data, along with the physical parameters of stars where the flares occurred, we developed a semiempirical grid that correlates a star's effective temperature and flare amplitude in TESS data with the flare's peak temperature. This allows interpolation of a flare's peak temperature based on the star's effective temperature (ranging from 2700 K to 4600 K) and flare amplitude from TESS observations. Applying this grid to 42 257 flares from TESS survey, we estimated peak flare temperatures between 5700 K and 38 300 K, with most flares showing peak blackbody temperatures around 11 100 ± 2400 K.