New Approach to Superflare Energy Determination

Abstract We present a new method for estimating the total energy radiated by stellar flares in broadband continua, which assumes a constant emitting area but incorporates a time-dependent temperature evolution. This physically motivated approach offers an alternative to the commonly used method that assumes a fixed flare temperature of about 10,000 K and a variable area. By allowing the temperature to vary over time while keeping the emitting area constant, our method captures more realistic flare behavior. This time-dependent treatment of the flare temperature is supported by numerous solar observations, numerical simulations, and multiwavelength studies of active stars. We demonstrate that using peak flare temperatures estimated from a semi-empirical model grid, rather than assuming an ad hoc flare temperature value, improves the accuracy of total energy estimates. Although the most precise results still require multiband photometry/spectroscopy or independently constrained flare temperatures, our method offers a practical and scalable solution for single-band observations. It is particularly well suited for main-sequence stars of spectral types K4 and later with known effective temperatures. Finally, we discuss how the flare continuum behaves under varying chromospheric conditions. Our method improves flare energy estimates by incorporating a physically relevant time-dependent temperature evolution and empirically derived peak temperatures, rather than assuming a constant 10,000 K value. This modification reduces systematic errors that can reach factors of up to 10 as compared to previous estimates. We proved this on a sample of 50,320 TESS flares.