MUSE observations of the lensing cluster Abell 1689

International audienceContext. This paper presents the results obtained with the Multi Unit Spectroscopic Explorer (MUSE) for the core of the lensing cluster Abell 1689, as part of MUSE's commissioning at the ESO Very Large Telescope. Aims. Integral-field observations with MUSE provide a unique view of the central 1 x 1 arcmin(2) region at intermediate spectral resolution in the visible domain, allowing us to conduct a complete census of both cluster galaxies and lensed background sources. Methods. We performed a spectroscopic analysis of all sources found in the MUSE data cube. Two hundred and eighty-two objects were systematically extracted from the cube based on a guided-and-manual approach. We also tested three different tools for the automated detection and extraction of line emitters. Cluster galaxies and lensed sources were identified based on their spectral features. We investigated the multiple-image configuration for all known sources in the field. Results. Previous to our survey, 28 different lensed galaxies displaying 46 multiple images were known in the MUSE field of view, most of them were detected through photometric redshifts and lensing considerations. Of these, we spectroscopically confirm 12 images based on their emission lines, corresponding to 7 different lensed galaxies between z = 0.95 and 5.0. In addition, 14 new galaxies have been spectroscopically identified in this area thanks to MUSE data, with redshifts ranging between 0.8 and 6.2. All background sources detected within the MUSE field of view correspond to multiple-imaged systems lensed by A1689. Seventeen sources in total are found at z \textgreater= 3 based on their Lyman-alpha emission, with Lyman-alpha luminosities ranging between 40.5 less than or similar to log(Ly alpha) less than or similar to 42.5 after correction for magnification. This sample is particularly sensitive to the slope of the luminosity function toward the faintest end. The density of sources obtained in this survey is consistent with a steep value of alpha \textless= -1.5, although this result still needs further investigation. Conclusions. These results illustrate the efficiency of MUSE in characterizing lensing clusters on one hand and in studying faint and distant populations of galaxies on the other hand. In particular, our current survey of lensing clusters is expected to provide a unique census of sources responsible for the reionization in a representative volume at z similar to 4-7