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 × 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 L_bol ≲ 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 M∗∼1011M⊙⁠. 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 L_bol > 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 L_bol ≲ 10⁴⁵ erg s⁻¹. At high redshifts, low-luminosity quasars are thus the best targets for understanding typical formation paths for SMBHs in galaxies.