  CARMENES is a spectrograph for radial velocity surveys of M dwarfs with the
aim of detecting Earth-mass planets orbiting in the habitable zones of their
host stars. To ensure an optimal use of the CARMENES Guaranteed Time
Observations, in this paper we investigate the correlation of activity and
rotation for approximately 2200 M dwarfs, ranging in spectral type from M0.0 V
to M9.0 V. We present new high-resolution spectroscopic observations with
FEROS, CAFE, and HRS of approximately 500 M dwarfs. For each new observation,
we determined its radial velocity and measured its Halpha activity index and
its rotation velocity. Additionally, we have multiple observations of many
stars to investigate if there are any radial velocity variations due to
multiplicity. The results of our survey confirm that early-M dwarfs are Halpha
inactive with low rotational velocities and that late-M dwarfs are Halpha
active with very high rotational velocities. The results of this
high-resolution analysis comprise the most extensive catalogue of rotation and
activity in M dwarfs currently available.
