EIGER VI. The Correlation Function, Host Halo Mass and Duty Cycle of Luminous Quasars at z6

We expect luminous (M₁₄₅₀-26. 5) high-redshift quasars to trace the highest density peaks in our universe, and therefore to reside in proto-clusters encompassing an abundance of galaxies in close vicinity. Here, we present observations of four z6 quasar fields using JWST/NIRCam in imaging and widefield slitless spectroscopy mode and report a wide range in the number of detected OIII-emitting galaxies in the quasars' environments, ranging between a density enhancement of >100 within a 2 cMpc radius - one of the largest proto-clusters during the Epoch of Reionization discovered to date - to a density contrast consistent with zero, indicating the presence of a UV-luminous quasar in a region comparable to the average density of the universe. By measuring the two-point cross-correlation function of quasars and their surrounding galaxies, as well as the galaxy auto-correlation function, we infer a correlation length of quasars at z=6. 25 of r₀^ QQ=21. 3^+2. 7-₂. ₆~ cMpc\, h^-1, while we obtain a correlation length of the OIII-emitting galaxies of r₀^ GG=4. 20. 1~ cMpc\, h^-1. By comparing the correlation functions to dark-matter-only simulations we estimate the minimum mass of the quasars' host dark matter halos to be ₁₀ (M ₇₀₋₎, ₌₈₍/M_) =12. 300. 14 (and ₁₀ (M ₇₀₋₎, ₌₈₍^ OIII/M_) = 10. 720. 03 for the OIII-emitters), indicating that (a) luminous quasars do not necessarily reside within the most overdense regions in the early universe, and that (b) the UV-luminous duty cycle of quasar activity at these redshifts is f ₃ₔₓₘ1. Such short quasar activity timescales challenge our understanding of early supermassive black hole growth and provide evidence for highly dust-obscured growth phases or episodic, radiatively inefficient accretion rates.