EIGER VI. The Correlation Function, Host Halo Mass and Duty Cycle of Luminous Quasars at z≳6

We expect luminous (M_1450≲-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 z≳6 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 δ>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 r_0^ QQ=21.3^+2.7_-2.6  cMpc h^-1, while we obtain a correlation length of the [OIII]-emitting galaxies of r_0^ GG=4.2±0.1  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 log_10(M_ halo, min/M_⊙)=12.30±0.14 (and log_10(M_ halo, min^ [OIII]/M_⊙) = 10.72±0.03 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_ duty≪1. 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.