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 L-bol = 5 x 10(46) ergs(-1), the z = 6 QLF is dominated by SMBHs that are at least 0.3 dex above the z = 6 median M-center dot-M-* relation. The QLF is dominated by typical SMBHs (i.e. within +/- 0.3 dex around the M-center dot-M-* relation) at L-bol less than or similar to 10(45) ergs(-1). At z similar to 6, the intrinsic M-center dot-M-* relation for all SMBHs is slightly steeper than the z = 0 scaling, with a similar normalization at . We also predict the M-center dot-M-* relation for z = 6 bright quasars selected by different bolometric luminosity thresholds, finding very good agreement with observations. For quasars with L-bol > 3 x 10(46) (10(48)) ergs(-1), the scaling relation is shifted upwards by similar to 0.35 (1.0) dex for 10(11)M(circle dot) galaxies. To accurately measure the intrinsic M-center dot-M-* relation, it is essential to include fainter quasars with L-bol less than or similar to 10(45) ergs(-1). At high redshifts, low-luminosity quasars are thus the best targets for understanding typical formation paths for SMBHs in galaxies.