The CARMENES search for exoplanets around M dwarfs. A homogeneous catalogue of projected rotational velocities accounting for limb darkening

Stellar rotation is closely linked to both the age and the magnetic activity of stars. Through gyrochronology, studying stellar rotation provides a means to estimate stellar ages and trace the evolution of planetary systems, and it is also a crucial means to constrain and correct stellar activity effects for robust exoplanet detection and characterisation. CARMENES is a dual-channel, high-resolution (mathcal R > 80000) spectrograph that has been highly successful in detecting exoplanets around M-dwarf stars using the radial-velocity technique, and it also enables precise measurements of the projected rotational velocity (v i) from spectral line broadening. We present an oversampled convolution method that incorporates a realistic limb-darkening model to determine v . We applied our method to 392 M dwarfs observed with CARMENES and it yielded v ) with a median relative uncertainty of 6.8,%, which is substantially smaller than the 15.4,% reported in the literature. This work provides the largest uniform catalogue of v i from CARMENES spectra by comparing observed spectra with that of a template star. The advantages over existing methods in the literature have been assessed using high-resolution synthetic spectra that span effective temperatures of 2500--4000,K and projected rotational velocities of up to 50,km,s -1 i measurements (or upper limits at 2,km,s -1 i measurements for M dwarfs, including significantly updated values for several targets, along with 36 new targets.