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We use the high-resolution cosmological simulation Illustris to investigatethe clustering of supermassive black holes across cosmic time, the link betweenblack hole clustering and host halo masses, and the implications for black holeduty cycles. Our predicted black hole correlation length and bias match theobservational data very well across the full redshift range probed. Black holeclustering is strongly luminosity-dependent on small, 1-halo scales, with somemoderate dependence on larger scales of a few Mpc at intermediate redshifts. Wefind black hole clustering to evolve only weakly with redshift, initiallyfollowing the behaviour of their hosts. However below z ~ 2 black holeclustering increases faster than that of their hosts, which leads to asignificant overestimate of the clustering-predicted host halo mass. The fulldistribution of host halo masses is very wide, including a low-mass tailextending up to an order of magnitude below the naive prediction for minimumhost mass. Our black hole duty cycles follow a power-law dependence on blackhole mass and decrease with redshift, and we provide accurate analytic fits tothese. The increase in clustering amplitude at late times, however, means thatduty cycle estimates based on black hole clustering can overestimate dutycycles substantially, by more than two orders of magnitude. We find the bestagreement when the minimum host mass is assumed to be $10^{11.2} M_\odot$ ,which provides an accurate measure across all redshifts and luminosity rangesprobed by our simulation.

Black hole clustering and duty cycles in the Illustris simulation