Flare Rates, Rotation Periods, and Spectroscopic Activity Indicators of a Volume-complete Sample of Mid- to Late-M Dwarfs within 15 pc

We present a study of flare rates, rotation periods, and spectroscopic activity indicators of 125 single stars within 15 parsecs and with masses between 0.1 and 0.3 M observed during the first year of the TESS mission, with the goal of elucidating the relationship between these various magnetically connected phenomena. We gathered multiepoch high-resolution spectra of each target, and we measured equivalent widths of the activity indicators helium I D-3, H alpha, and the calcium infrared triplet line at 8542.09 A. We present 18 new rotation periods from MEarth photometry and 19 new rotation periods from TESS photometry. We present a catalog of 1392 flares. After correcting for sensitivity, we find the slope of the flare frequency distribution for all stars to have a standard value of alpha = 1.98 0.02. We determine R-31.5, the rate of flares per day with energies above E = 3.16 x 10(31) ergs in the TESS bandpass. We find that below a critical value of H alpha EW = -0.71 A, log R-31.5 increases linearly with increasing H alpha emission; above this value, log R-31.5 declines rapidly. The stars divide into two groups: 26% have H alpha in emission, high flare rates with typical values of log R-31.5 = -1.30 0.08, and have Rossby numbers alpha in emission and exhibit log R-31.5 < -3.86, with the majority of these stars not showing a single flare during the TESS observations.