SPIDERS: the spectroscopic follow-up of X-ray selected clusters of galaxies in SDSS-IV

SPIDERS (The SPectroscopic IDentification of eROSITA Sources) is a program dedicated to the homogeneous and complete spectroscopic follow-up of X-ray AGN and galaxy clusters over a large area ($\sim$7500 deg$^2$) of the extragalactic sky. SPIDERS is part of the SDSS-IV project, together with the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) and the Time-Domain Spectroscopic Survey (TDSS). This paper describes the largest project within SPIDERS before the launch of eROSITA: an optical spectroscopic survey of X-ray selected, massive ($\sim 10^{14}$ to $10^{15}~M_{\odot}$) galaxy clusters discovered in ROSAT and XMM-Newton imaging. The immediate aim is to determine precise ($\Delta_z \sim 0.001$) redshifts for 4,000-5,000 of these systems out to $z \sim 0.6$. The scientific goal of the program is precision cosmology, using clusters as probes of large-scale structure in the expanding Universe. We present the cluster samples, target selection algorithms and observation strategies. We demonstrate the efficiency of selecting targets using a combination of SDSS imaging data, a robust red-sequence finder and a dedicated prioritization scheme. We describe a set of algorithms and work-flow developed to collate spectra and assign cluster membership, and to deliver catalogues of spectroscopically confirmed clusters. We discuss the relevance of line-of-sight velocity dispersion estimators for the richer systems. We illustrate our techniques by constructing a catalogue of 230 spectroscopically validated clusters ($0.031 < z < 0.658$), found in pilot observations. We discuss two potential science applications of the SPIDERS sample: the study of the X-ray luminosity-velocity dispersion ($L_X-\sigma$) relation and the building of stacked phase-space diagrams.