TRINITY II: The Luminosity-dependent Bias of the Supermassive Black Hole Mass--Galaxy Mass Relation for Bright Quasars at $z=6$

Abstract

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 $L_{\mathrm{bol}}=5\times 10^{46}$ erg/s, the $z=6$ QLF is dominated by SMBHs that are at least 0.3 dex above the $z=6$ median $M_{\bullet }-M_{\ast }$ relation. The QLF is dominated by typical SMBHs (i.e., within $\pm 0.3$ dex around the $M_{\bullet }-M_{\ast }$ relation) at $L_{\mathrm{bol}}\lesssim 10^{45}$ erg/s. At $z\sim 6$, the intrinsic $M_{\bullet }-M_{\ast }$ relation for all SMBHs is slightly steeper than the $z=0$ scaling, with a similar normalization at $M_{\ast }\sim 10^{11}{M}_{\odot }$. We also predict the $M_{\bullet }-M_{\ast }$ relation for $z=6$ bright quasars selected by different bolometric luminosity thresholds, finding very good agreement with observations. For quasars with $L_{\mathrm{bol}}>3\times 10^{46}$ ($10^{48}$) erg/s, the scaling relation is shifted upwards by $\sim 0.35$ (1.0) dex for $10^{11}{M}_{\odot }$ galaxies. To accurately measure the intrinsic $M_{\bullet }-M_{\ast }$ relation, it is essential to include fainter quasars with $L_{\mathrm{bol}}\lesssim 10^{45}$ erg/s. At high redshifts, low-luminosity quasars are thus the best targets for understanding typical formation paths for SMBHs in galaxies.

5 pages, 3 figures. Submitted to MNRAS Letters. Comments welcome!