Flares and rotation periods of CARMENES M dwarfs from TESS data

CARMENES is a spectrograph built for the 3.5 m telescope at the Calar Alto Observatory. The main aim is to detect low mass planets around M dwarfs. In order to achieve this goal, it is critical to characterize the monitored stars, especially their activity and rotation. Using Quick-Look Pipeline TESS data from its first two cycles, we studied the rotation and activity in the 2-min cadence time series of 1249 M dwarfs in the CARMENES input catalog. Next, with generalised Lomb-Scargle (GLS) periodograms, we measured 231 rotation periods between 0.11 d and 10.52 d. Of them, 147 are consistent with their literature counterparts and 74 were previously unknown. Using splines and Fourier polynomials, we detrended the light curves of the stars for which we found a rotational period in order to look for flaring activity. We measured energies between ${10}^{30}$ erg and ${10}^{35}$ erg of 1922 flares of 225 periodic M dwarfs. We fitted the cumulative frequency distribution  of flares with energies greater than ${10}^{33}$ erg to a power law of the form $NdE\propto E^{-\alpha }dE$ and determined $\alpha ={2.119}_{-0.105}^{+0.075}$. We also found α to increase for later spectral types.