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Kepler Flares I. Active and Inactive M dwarfs

We analyzed Kepler short-cadence M dwarf observations. Spectra from the ARC 3.5m telescope identify magnetically active (H$α$ in emission) stars. The active stars are of mid-M spectral type, have numerous flares, and well-defined rotational modulation due to starspots. The inactive stars are of early-M type, exhibit less starspot signature, and have fewer flares. A Kepler to U-band energy scaling allows comparison of the Kepler flare frequency distributions with previous ground-based data. M dwarfs span a large range of flare frequency and energy, blurring the distinction between active and inactive stars designated solely by the presence of H$α$. We analyzed classical and complex (multiple peak) flares on GJ 1243, finding strong correlations between flare energy, amplitude, duration and decay time, with only a weak dependence on rise time. Complex flares last longer and have higher energy at the same amplitude, and higher energy flares are more likely to be complex. A power law fits the energy distribution for flares with log $E_{K_p} >$ 31 ergs, but the predicted number of low energy flares far exceeds the number observed, at energies where flares are still easily detectable, indicating that the power law distribution may flatten at low energy. There is no correlation of flare occurrence or energy with starspot phase; the flare waiting time distribution is consistent with flares occurring randomly in time; and the energies of consecutive flares are uncorrelated. These observations support a scenario where many independent active regions on the stellar surface are contributing to the observed flare rate.