Is there Na I in the atmosphere of HD 209458b?: Effect of the centre-to-limb variation and Rossiter-McLaughlin effect in transmission spectroscopy studies

Based on observations made with the Italian Telescopio Nazionale Galileo (TNG) operated on the island of La Palma by the Fundacion Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. CARMENES is an instrument for the Centro Astronomico Hispano-Aleman de Calar Alto (CAHA, Almeria, Spain). CARMENES is funded by the German Max-Planck-Gesellschaft (MPG), the Spanish Consejo Superior de Investigaciones Cientificas (CSIC), the European Union through FEDER/ERF FICTS-2011-02 funds, and the members of the CARMENES Consortium (Max-Planck-Institut fur Astronomie, Instituto de Astrofisica de Andalucia, Landessternwarte Konigstuhl, Institut de Ciencies de l'Espai, Insitut fur Astrophysik Gottingen, Universidad Complutense de Madrid, Thuringer Landessternwarte Tautenburg, Instituto de Astrofisica de Canarias, Hamburger Sternwarte, Centro de Astrobiologia and Centro Astronomico Hispano- Aleman), with additional contributions by the Spanish Ministry of Economy, the German Science Foundation through the Major Research Instrumentation Programme and DFG Research Unit FOR2544 "Blue Planets around Red Stars", the Klaus Tschira Stiftung, the states of Baden-Wurttemberg and Niedersachsen, and by the Junta de Andalucia. This work is partly financed by the Spanish Ministry of Economics and Competitiveness through project ESP2016-80435-C2-2-R and ESP2017-87143-R. G.C. acknowledges the support by the Natural Science Foundation of Jiangsu Province (Grant No. BK20190110), the National Natural Science Foundation of China (Grant No. 11503088, 11573073, 11573075). F.Y. acknowledges the support of the DFG priority program SPP 1992 "Exploring the Diversity of Extrasolar Planets (RE 1664/16-1)". This work made use of PyAstronomy and of the VALD database, operated at Uppsala University, the Institute of Astronomy RAS in Moscow, and the University of Vienna.