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ABSTRACT Recent observations from the EIGER JWST program have measured for the first time the quasar–galaxy cross-correlation function at $$z\approx 6$$. The autocorrelation function of faint $$z\approx 6$$ quasars was also recently estimated. These measurements provide key insights into the properties of quasars and galaxies at high redshift and their relation with the host dark matter haloes. In this work, we interpret these data building upon an empirical quasar population model that has been applied successfully to quasar clustering and demographic measurements at $$z\approx 2\!-\!4$$. We use a new, large-volume N-body simulation with more than a trillion particles, FLAMINGO-10k, to model quasars and galaxies simultaneously. We successfully reproduce observations of $$z\approx 6$$ quasars and galaxies (i.e. their clustering properties and luminosity functions), and infer key quantities such as their luminosity–halo mass relation, the mass function of their host haloes, and their duty cycle/occupation fraction. Our key findings are (i) quasars reside on average in $$\approx 10^{12.5}\, {\rm M}_{\odot }$$ haloes (corresponding to $$\approx 5\sigma$$ fluctuations in the initial conditions of the linear density field), but the distribution of host halo masses is quite broad; (ii) the duty cycle of (UV-bright) quasar activity is relatively low ($$\approx 1~{{\ \rm per\ cent}}$$); (iii) galaxies (that are bright in [O iii]) live in much smaller haloes ($$\approx 10^{10.9}\, {\rm M}_{\odot }$$) and have a larger duty cycle (occupation fraction) of $$\approx 13~{{\ \rm per\ cent}}$$. Finally, we focus on the inferred properties of quasars and present a homogeneous analysis of their evolution with redshift. The picture that emerges reveals a strong evolution of the host halo mass and duty cycle of quasars at $$z\approx 2\!-\!6$$, and calls for new investigations of the role of quasar activity across cosmic time. 

Abstract Over the next 5 yr, the Dark Energy Spectroscopic Instrument (DESI) will use 10 spectrographs with 5000 fibers on the 4 m Mayall Telescope at Kitt Peak National Observatory to conduct the first Stage IV dark energy galaxy survey. Atz< 0.6, the DESI Bright Galaxy Survey (BGS) will produce the most detailed map of the universe during the dark-energy-dominated epoch with redshifts of >10 million galaxies spanning 14,000 deg². In this work, we present and validate the final BGS target selection and survey design. From the Legacy Surveys, BGS will target anr< 19.5 mag limited sample (BGS Bright), a fainter 19.5 <r< 20.175 color-selected sample (BGS Faint), and a smaller low-zquasar sample. BGS will observe these targets using exposure times scaled to achieve homogeneous completeness and cover the footprint three times. We use observations from the Survey Validation programs conducted prior to the main survey along with simulations to show that BGS can complete its strategy and make optimal use of “bright” time. BGS targets have stellar contamination <1%, and their densities do not depend strongly on imaging properties. BGS Bright will achieve >80% fiber assignment efficiency. Finally, BGS Bright and BGS Faint will achieve >95% redshift success over any observing condition. BGS meets the requirements for an extensive range of scientific applications. BGS will yield the most precise baryon acoustic oscillation and redshift-space distortion measurements atz< 0.4. It presents opportunities for new methods that require highly complete and dense samples (e.g.,N-point statistics, multitracers). BGS further provides a powerful tool to study galaxy populations and the relations between galaxies and dark matter.