  We present a study of the activity-rotation relation for M dwarf stars, using
new X-ray data from the ROentgen Survey with an Imaging Telescope Array
(eROSITA) on board the Russian Spektrum-Roentgen-Gamma mission (SRG), combined
with photometric rotation periods from the Transiting Exoplanet Survey
Satellite (TESS). The stars used in this work are selected from the superblink
proper motion catalog of nearby M dwarfs. We study the 135 stars with both a
detection in the first eROSITA survey (eRASS1) and a rotation period
measurement from TESS jointly with the sample of 197 superblink M dwarfs
re-adapted from our previous work. We fit the activity-rotation relation for
stars with rotation periods shorter than ~10 d (saturated regime) using three
mass bins. The surprising positive slope for stars in our lowest mass bin
($M_{\star} \leq 0.4 {\rm M_\odot}$) is due to a paucity of stars with
intermediate rotation periods (~ 1-10 d), probably caused by fast period
evolution. The much higher fraction of eRASS1 detections compared to stars that
have also rotation periods from TESS shows that eROSITA is also sensitive for
slower rotating M dwarfs that are in the unsaturated regime with periods
inaccessible to TESS.
