Trinity II: The luminosity-dependent bias of the supermassive black hole mass-galaxy mass relation for bright quasars at z = 6

Using recent empirical constraints on the dark matter halo-galaxy-supermassive black hole (SMBH) connection from z = 0-7, we infer how undermassive, typical, and overmassive SMBHs contribute to the quasar luminosity function (QLF) at z = 6. We find that beyond Lbol = 5 × 1046 erg s-1, the z = 6 QLF is dominated by SMBHs that are at least 0.3 dex above the z = 6 median M•-M∗ relation. The QLF is dominated by typical SMBHs (i.e. within ±0.3 dex around the M•-M∗ relation) at Lbol 1045 erg s-1. At z ∼6, the intrinsic M•-M∗ relation for all SMBHs is slightly steeper than the z = 0 scaling, with a similar normalization at. We also predict the M•-M∗ relation for z = 6 bright quasars selected by different bolometric luminosity thresholds, finding very good agreement with observations. For quasars with Lbol > 3 × 1046 (1048) erg s-1, the scaling relation is shifted upwards by ∼0.35 (1.0) dex for 1011M galaxies. To accurately measure the intrinsic M•-M∗ relation, it is essential to include fainter quasars with Lbol 1045 erg s-1. At high redshifts, low-luminosity quasars are thus the best targets for understanding typical formation paths for SMBHs in galaxies.