Effective flare temperature for 200+ flares observed on 69 FGK-type stars

Assuming that the spectrum of white-light flares (WLFs) can be described by blackbody radiation, we determined the effective flare temperature for over 200 flares observed by CoRoT on 69 stars with spectral types F, G, and K. The flare temperature is obtained from the flare equivalent duration and stellar flux in the Blue and Red CoRoT light curves. The wavelength limits for the Blue and Red channels were estimated using spectra from the Pickles library for the spectral type and luminosity class of the star provided by the Exodat Database. We took the uncertainty in the stellar classification into account and carefully propagated it in our estimate of the flare temperature, obtaining uncertainties between 10% and 30%. We estimated the flare temperature probability density function using the kernel density estimator method and obtained a mode equal to 5,300 K. 75% of the highest density interval is between 3,400 and 8,100 K. The WLF spectrum is described often as a blackbody with a temperature of 9,000 or 10,000 K. Nonetheless, our results agree with recent solar WLF temperature estimations between 5,000 and 7,000 K.

We took advantage of the fact that the Gaia G band is very similar to the CoRoT White channel and that most of our stars were observed by Gaia EDR3 to calibrate the CoRoT White flux with the Gaia high-precision photometry. The flare peak amplitude corresponds to 2.5% of the stellar flux in the Gaia G band. The Gaia flare energy is calculated by multiplying the flare equivalent duration by the stellar luminosity in the Gaia G band. The Gaia flare energies (E) vary from 10³² to 10³⁷ ergs. We do not observe any correlation with the flare temperature. Assuming that the flare duration is proportional to E^1/3 B^-5/3 (Namekata et al. 2017), we notice that stars with a rotation period smaller than one day have a magnetic field (B) twice as large as those with rotation between 10 and 20 days.