# Early black holes in cosmological simulations: luminosity functions and clustering behaviour

We examine predictions for the quasar luminosity functions (QLFs) and quasar clustering at high redshift (*z* ≥ 4.75) using *MassiveBlack*, our new hydrodynamic cosmological simulation which includes a self-consistent model for black hole (BH) growth and feedback. We show that the model reproduces the Sloan QLF within observational constraints at *z* ≥ 5. We find that the high-*z* QLF is consistent with a redshift-independent occupation distribution of BHs among dark matter haloes (which we provide) such that the evolution of the QLF follows that of the halo mass function. The sole exception is the bright end at *z* = 6 and 7, where BHs in high-mass haloes tend to be unusually bright due to extended periods of Eddington growth caused by high-density cold flows into the halo centre. We further use these luminosity functions to make predictions for the number density of quasars in upcoming surveys, predicting that there should be ∼119 ± 28 (∼87 ± 28) quasars detectable in the *F*125*W* band of the WIDE (DEEP) fields of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) from *z* = 5 to 6, ∼19 ± 7 (∼18 ± 9) from *z* = 6 to 7 and ∼1.7 ± 1.5 (∼1.5 ± 1.5) from *z* = 7 to 8. We also investigate quasar clustering, finding that the correlation length is fully consistent with current constraints for Sloan quasars (*r*_{0} ∼ 17 *h*^{−1} Mpc at *z*= 4 for quasars above *m*_{i} = 20.2) and grows slowly with redshift up to *z* = 6 (*r*_{0} ∼ 22 *h*^{−1} Mpc). Finally, we note that the quasar clustering strength depends weakly on luminosity for low *L*_{BH}, but gets stronger at higher *L*_{BH}as the BHs are found in higher mass haloes.