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Galactic Kinematics and Observed Flare Rates of a Volume-Complete Sample of Mid-to-Late M-dwarfs: Constraints on the History of the Stellar Radiation Environment of Planets Orbiting Low-mass Stars

We present a study of the relationship between galactic kinematics, flare rates, chromospheric activity, and rotation periods for a volume-complete, nearly all-sky sample of 219 single stars within 15 parsecs and with masses between 0.1$-$0.3 M$_{odot}l$ observed during the primary mission of TESS. We find all stars are consistent with a common value of $α$=1.984 $\pm$ 0.019 for the exponent of the flare frequency distribution. Using our measured stellar radial velocities and Gaia astrometry, we determine galactic UVW space motions. We find 64% of stars are members of the Galactic thin disk, 5% belong to the thick disk, and for the remaining 31%, we cannot confidently assign membership to either component. If we assume star formation has been constant in the thin disk for the past 8 Gyr, then based on the fraction that we observe to be active, we estimate the average age at which these stars transition from the saturated to the unsaturated flaring regime to be 2.4 $\pm$ 0.3 Gyr. This is consistent with the ages that we assign from galactic kinematics: We find that stars with Prot $<$ 10 days have an age of 2.0 $\pm$ 1.2 Gyr, stars with 10 $<$ Prot $\leq$ 90 days have an age of 5.6 $\pm$ 2.7 Gyr, and stars with Prot $>$ 90 days have an age of 12.9 $\pm$ 3.5 Gyr. We find that the average age of stars with Prot $<$ 10 days increases with decreasing stellar mass from 0.6 $\pm$ 0.3 Gyr (0.2 - 0.3 M$_{odot}$) to 2.3 $\pm$ 1.3 Gyr (0.1--0.2 M$_{odot}l$).