The narrowest M-dwarf line profiles and the rotation-activity connection at very slow rotation

Context. The rotation-activity connection explains stellar activity in terms of rotation and convective overturn time. It is well established in stars of spectral types F-K as well as in M-type stars of young clusters, in which rotation is still very rapid even among M-dwarfs. The rotation-activity connection is not established in field M-dwarfs, because they rotate very slowly, and detecting rotation periods or rotational line broadening is a challenge. In field M-dwarfs, saturation sets in below upsilon(rot) = 5 km s(-1), hence they are expected to populate the non-saturated part of the rotation-activity connection. Aims. This work for the first time shows intrinsically resolved spectral lines of slowly rotating M-dwarfs and makes a first comparison to estimates of convective velocities. By measuring rotation velocities in a sample of mostly inactive M-dwarfs, the unsaturated part of the rotation-activity connection is followed into the regime of very low activity. Methods. Spectra of ten M-dwarfs are taken at a resolving power of R = 200 000 at the CES in the near infrared region where molecular FeH has strong absorption bands. The intrinsically very narrow lines are compared to model calculations of convective flows, and rotational broadening is measured. Results. In one star, an upper limit of upsilon sin i = 1 km s(-1) was found, significant rotation was detected in the other nine objects. All inactive stars show rotation below or equal to 2 km s(-1). In the two active stars AD Leo and YZ CMi, rotation velocities are found to be 40-50% below the results from earlier studies. Conclusions. The rotation activity connection holds in field early-M stars, too. Activity and rotation velocities of the sample stars are well in agreement with the relation found in earlier and younger stars. The intrinsic absorption profiles of molecular FeH lines are consistent with calculations from atomic Fe lines. Investigation of FeH line profiles is a very promising tool to measure convection patterns at the surfaces of M-stars.