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

We expect luminous (M-1450 less than or similar to -26.5) high-redshift quasars to trace the highest-density peaks in the early Universe. Here, we present observations of four z greater than or similar to 6 quasar fields using JWST/NIRCam in the imaging and wide-field slitless spectroscopy mode and report a wide range in the number of detected [O iii]-emitting galaxies in the quasars' environments, ranging between a density enhancement of delta approximate to 65 within a 2 cMpc radius-one of the largest protoclusters 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 autocorrelation function, we infer a correlation length of quasars at < z > = 6.25 of r(0)(QQ)=22.0(-2.9)(+3.0)cMpch(-1), while we obtain a correlation length of the [O iii]-emitting galaxies of r0GG=4.1 +/- 0.3cMpch-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 log10(M-halo,M-min/M-circle dot)=12.43-0.15+0.13 (and log10(M-halo,M-min[OIII]/M-circle dot)=10.56(-0.03)(+0.05) for the [O iii] 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.