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Understanding the links between the activity of supermassive black holes (SMBHs) at the centres of galaxies and their host dark matter haloes is a key question in modern astrophysics. The final data release of the SDSS-IV eBOSS provides the largest contemporary spectroscopic sample of galaxies and quasi-stellar objects (QSOs). Using this sample and covering the redshift interval z = 0.7–1.1, we have measured the clustering properties of the eBOSS QSOs, emission-line galaxies (ELGs), and luminous red galaxies (LRGs). We have also measured the fraction of QSOs as a function of the overdensity defined by the galaxy population. Using these measurements, we investigate how QSOs populate and sample the galaxy population, and how the host dark-matter haloes of QSOs sample the underlying halo distribution. We find that the probability of a galaxy hosting a QSO is independent of the host dark matter halo mass of the galaxy. We also find that about 60 per cent of eBOSS QSOs are hosted by LRGs and about 20–40 per cent of QSOs are hosted by satellite galaxies. We find a slight preference for QSOs to populate satellite galaxies over central galaxies. This is connected to the host halo mass distribution of different types of galaxies. Based on our analysis, QSOs should be hosted by a very broad distribution of haloes, and their occurrence should be modulated only by the efficiency of galaxy formation processes.