X-ray/H$α$ scaling relationships in stellar flares

Abstract

We report on the results of our simultaneous observations of three large stellar flares with soft X-rays (SXRs) and an H$\mathrmα$ emission line from two binary systems of RS CVn type. The energies released in the X-ray and H$\mathrmα$ emissions during the flares were $10^{36}$--$10^{38}$ and $10^{35}$--$10^{37}$ erg, respectively. It renders the set of the observations as the first successful simultaneous X-ray/H$\mathrmα$ observations of the stellar flares with energies above $10^{35}$ erg; although the coverage of the H$\mathrmα$ observations of the stellar flares with energies above $10^{35}$ erg; although the coverage of the H$\mathrmα$ observations was limited, with $\sim$10\% of the $e$-folding time in the decay phase of the flares, that of the SXR ones was complete. Combining the obtained physical parameters and those in literature for solar and stellar flares, we obtained a good proportional relation between the emitted energies of X-ray and H$\mathrmα$ emissions for a flare energy range of $10^{29}$--$10^{38}$ erg. The ratio of the H$\mathrmα$-line to bolometric X-ray emissions was $\sim$0.1, where the latter was estimated by converting the observed SXR emission to that in the 0.1--100 keV band according to the best-fitting thin thermal model. We also found that the $e$-folding times of the SXR and H$\mathrmα$ light curves in the decaying phase of a flare are in agreement for a time range of $1$--$10^4$~s. Even very large stellar flares with energies of six orders of magnitude larger than the most energetic solar flares follow the same scaling relationships with solar and much less energetic stellar flares. This fact suggests that their physical parameters can be estimated on the basis of the known physics of solar and stellar flares.