SPIDERS: overview of the X-ray galaxy cluster follow-up and the final spectroscopic data release

SPIDERS (The SPectroscopic IDentification of eROSITA Sources) is a large spectroscopic programme for X-ray selected galaxy clusters as part of the Sloan Digital Sky Survey-IV (SDSS-IV). We describe the final data set in the context of SDSS Data Release 16 (DR16): the survey overall characteristics, final targeting strategies, achieved completeness, and spectral quality, with special emphasis on its use as a galaxy cluster sample for cosmology applications. SPIDERS now consists of about 27 000 new optical spectra of galaxies selected within 4000 photometric red sequences, each associated with an X-ray source. The excellent spectrograph efficiency and a robust analysis pipeline yield a spectroscopic redshift measurement success rate exceeding 98 per cent, with a median velocity accuracy of 20 km s^-1 (at z = 0.2). Using the catalogue of 2740 X-ray galaxy clusters confirmed with DR16 spectroscopy, we reveal the 3D map of the galaxy cluster distribution in the observable Universe up to z ~ 0.6. We highlight the homogeneity of the member galaxy spectra among distinct regions of the galaxy cluster phase space. Aided by accurate spectroscopic redshifts and by a model of the sample selection effects, we compute the galaxy cluster X-ray luminosity function and we present its lack of evolution up to z = 0.6. Finally we discuss the prospects of forthcoming large multiplexed spectroscopic programmes dedicated to follow up the next generation of all-sky X-ray source catalogues.