Are coronae of magnetically active stars heated by flares?: II.: Extreme ultraviolet and X-ray flare statistics and the differential emission measure distribution

We investigate the EUV and X-ray are rate distribution in radiated energy of the late-type active star AD Leo. Occurrence rates of solar flares have previously been found to be distributed in energy according to a power law, dN/dE proportional to E-alpha with a power-law index alpha in the range 1.5-2.6. If alpha greater than or equal to 2, then an extrapolation of the are distribution to low are energies may be sufficient to heat the complete observable X-ray/EUV corona. We have obtained long observations of AD Leo with the EUVE and BeppoSAX satellites. Numerous flares have been detected, ranging over almost 2 orders of magnitude in their radiated energy. We compare the observed light curves with light curves synthesized from model flares that are distributed in energy according to a power law with selectable index alpha. Two methods are applied, the first comparing flux distributions of the binned data and the second using the distributions of photon arrival time differences in the unbinned data (for EUVE). Subsets of the light curves are tested individually, and the quiescent flux has optionally been treated as a superposition of flares from the same are distribution. We find acceptable alpha values between 2.0 and 2.5 for the EUVE DS and the BeppoSAX LECS data. Some variation is found depending on whether or not a strong and long-lasting are occurring in the EUVE data is included. The BeppoSAX MECS data indicate a somewhat shallower energy distribution (smaller alpha) than the simultaneously observed LECS data, which is attributed to the harder range of sensitivity of the MECS detector and the increasing peak temperatures of flares with increasing total (radiative) energy. The results suggest that flares can play an important role in the energy release of this active corona. We discuss caveats related to time variability, total energy, and multiple power-law distributions. Studying the limiting case of a corona that is entirely heated by a population of flares, we derive an expression for the time-averaged coronal differential emission measure distribution (DEM) that can be used as a diagnostic for the are energy distribution. The shape of the analytical DEM agrees with previously published DEMs from observations of active stars.