EvryFlare II: Rotation Periods of the Cool Flare Stars in TESS Across Half the Southern Sky.

We measure rotation periods and sinusoidal amplitudes in Evryscope light curves for 122 two-minute K5-M4 TESS targets selected for strong flaring. The Evryscope array of telescopes has observed all bright nearby stars in the South, producing two-minute cadence light curves since 2016. Long-term, high-cadence observations of rotating flare stars probe the complex relationship between stellar rotation, starspots, and superflares. We detect periods from 0.3487 to 104 d, and observe amplitudes from 0.008 to 0.216 g' mag. We find the Evryscope amplitudes are larger than those in TESS with the effect correlated to stellar mass (p-value=0.01). We compute the Rossby number (Ro), and find our sample selected for flaring has twice as many intermediate rotators (0.04 0.44) rotators; this may be astrophysical or a result of period-detection sensitivity. We discover 30 fast, 59 intermediate, and 33 slow rotators. We measure a median starspot coverage of 13% of the stellar hemisphere and constrain the minimum magnetic field strength consistent with our flare energies and spot coverage to be 500 G, with later-type stars exhibiting lower values than earlier-types. We observe a possible change in superflare rates at intermediate periods. However, we do not conclusively confirm the increased activity of intermediate rotators seen in previous studies. We split all rotators at Ro~0.2 into Prot 10 d bins to confirm short-period rotators exhibit higher superflare rates, larger flare energies, and higher starspot coverage than do long-period rotators, at p-values of 3.2 X 10^-5, 1.0 X 10^-5, and 0.01, respectively.