© ESO 2020Bauer, F. F.Zechmeister, M.Kaminski, A.Rodríguez López, C.Caballero, J. A.Azzaro, M.Stahl, S.Kossakowski, D.Quirrenbach, A.Becerril Jarque, S.Rodríguez, E.Amado, P. J.Seifert, W.Reiners, A.Schäfer, S.Ribas, I.Béjar, V. J. S.Cortés Contreras, M.Dreizler, S.Hatzes, A.Henning, T.Jeffers, S. V.Kürster, M.Lafarga, M.Montes, D.Morales, J. C.Schmitt, H. M. M.Schweitzer, A.Solano, EnriqueUnidad de Excelencia Científica María de Maeztu Centro de Astrobiología del Instituto Nacional de Técnica Aeroespacial y CSIC, MDM-2017-0737Centros de Excelencia Severo Ochoa, INSTITUTO DE ASTROFISICA DE ANDALUCIA (IAA), SEV-2017-0709Centros de Excelencia Severo Ochoa, INSTITUTO DE ASTROFÍSICA DE CANARIAS (IAC), SEV-2015-05482021-04-082021-04-082020-08-10Astronomy & Astrophysics 640: A50 (2020)0004-6361https://www.aanda.org/articles/aa/abs/2020/08/aa38031-20/aa38031-20.htmlhttp://hdl.handle.net/20.500.12666/142The high-resolution, dual channel, visible and near-infrared spectrograph CARMENES offers exciting opportunities for stellar and exoplanetary research on M dwarfs. In this work we address the challenge of reaching the highest radial velocity precision possible with a complex, actively cooled, cryogenic instrument, such as the near-infrared channel. We describe the performance of the instrument and the work flow used to derive precise Doppler measurements from the spectra. The capability of both CARMENES channels to detect small exoplanets is demonstrated with the example of the nearby M5.0 V star CD Cet (GJ 1057), around which we announce a super-Earth (4.0 ± 0.4 M· ) companion on a 2.29 d orbit. © 2020 ESO.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttps://creativecommons.org/licenses/by-nc-nd/4.0/Planetary systemsStars: individual: CD CetStars: late-TypeTechniques: radial velocitiesinfo:eu-repo/semantics/article10.1051/0004-6361/2020380311432-0746http://dx.doi.org/10.13039/501100000781info:eu-repo/semantics/openAccess