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 D₃, Hα, and the calcium infrared triplet line at 8542.09 Å. 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 α = 1.98 ± 0.02. We determine R_31.5, the rate of flares per day with energies above E = 3.16 × 10³¹ ergs in the TESS bandpass. We find that below a critical value of Hα EW = -0.71 Å, log R_31.5 increases linearly with increasing Hα emission; above this value, log R_31.5 declines rapidly. The stars divide into two groups: 26% have Hα in emission, high flare rates with typical values of log R_31.5 = -1.30 ± 0.08, and have Rossby numbers <0.50. The remaining 74% show little to no Hα 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.