Observational signs of limited flare area variation and peak flare temperature estimations in main-sequence flaring stars

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.