Context. Stellar rotation is a fundamental parameter in studies of the formation and evolution of stars. However, large homogeneous catalogues of rotational velocities derived from high-resolution stellar spectra are still lacking.
Aims. The main objective of this work is to determine the line-broadening parameter (Vbroad), which is a proxy for the stellar rotational velocity, in a large sample of FGKM stars based on their ESO/FEROS spectra. All these stars were previously parameterised by the AMBRE Project.
Methods. The line-broadening parameter was estimated by cross-correlating the FEROS spectra with binary masks, specifically chosen on the basis of the AMBRE stellar parameters. This methodology also relies on a specific calibration of a coupling constant between the rotational velocity and the width of the cross-correlation function. This fundamental step was performed by adopting the AMBRE grid of synthetic spectra. The derived Vbroad were then validated using data from the literature, ground-based spectroscopic surveys, and Gaia/RVS.
Results. After analysing more than 5000 FEROS spectra (including repeated spectra for several stars), we obtained the line-broadening coefficients for 2584 stars covering the FGKM spectral types, any stellar gravity, and metallicities between the metal-poor up to sub-solar regimes. The mean Vbroad relative uncertainty of this sample was found to be smaller than 8%. As expected, most stars were found to be slow rotators (below a few km/s), in particular, cool dwarfs and giants. However, several hot dwarfs and high-luminosity stars with high-Vbroad rates were identified, most of them not previously classified as fast rotators and/or affected by large macro-turbulent effects before the present work.
Conclusions. The measured rotational broadening values are of high-quality and verified on the basis of literature comparisons. We publicly provide this catalogue of line-broadening parameters, including stellar atmospheric and quality parameters, for the analysed AMBRE/FEROS sources.

line: profiles / catalogs / stars: rotation