Statistical Properties of Flare Variability, Energy, and Frequency in Low-Mass Stars

Although stellar flares have a long history of observations, there are few concrete understanding about underlying physical processes and meaningful correlations with other stellar properties. Most of previous observations dealt with only a small number of sample stars, and therefore not sufficient to support generalized statistical studies. Based on one-month long MMT time-series observations of the open cluster M37, we monitored light variations of nearly 2,500 M-dwarf stars and successfully identified 606 flare events from 422 stars. This is a rare attempt to estimate true flare rates and properties among many stars of the same age and mass group. For each flare, we considered both observational and physical parameters including flare shape, duration before and after the peak, baseline magnitude before and after the peak, peak magnitudes, total energy and peak energy, etc. We find significant correlations between some of key parameters over a wide range of energy ($Er=10^{32}{\sim}10^{36}ergs$). For instance, regardless of stellar luminosities, the energy power spectrum of flares can be approximated by a power law (${\beta}=0.83-0.97$). This suggests that flares follow similar physical mechanisms for atmospheric heating and cooling among these low-mass stars. From this MMT data set, we derived an average flaring rate of $0.019 hr^{-1}$ among flare stars and $0.003 hr^{-1}$ for all M-dwarf candidates. We will report the details of our analysis and discuss physical implications.