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 the early Universe. Here, we present observations of four z ≳ 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 δ ≈ 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 cMpc h − 1 , while we obtain a correlation length of the [O iii]-emitting galaxies of r 0 GG = 4.1 ± 0.3 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 ⊙ ) = 12.43 − 0.15 + 0.13 (and log 10 ( M halo , min [ OIII ] / M ⊙ ) = 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.