TRINITY IV: predictions for supermassive black holes at z ≳ 6

We present predictions for the high-redshift halo-galaxy-supermassive black hole (SMBH) connection from the TRINITY model. Matching a comprehensive compilation of galaxy (0 ≤ z ≤ 13) and SMBH data sets (0 ≤ z ≤ 6.5), TRINITY finds: (1) The number of SMBHs with M_• > 10⁹ M_⊙ in the observable Universe increases by five orders of magnitude from z ~ 10 to z ~ 2, and by another factor of ~3 from z ~ 2 to z = 0; (2) The M_• > 10⁹ and 10¹⁰ M_⊙ SMBHs at z ~ 6 live in haloes with ~(2 - 3) and (3 - 5) × 10¹² M_⊙; (3) the newly discovered JWST AGN candidates at 7 ≲ z ≲ 11 are overmassive compared to the intrinsic SMBH mass-galaxy mass relation from TRINITY, but they are still broadly consistent with TRINITY predictions for flux limited AGN samples with Lauer bias. This bias favours the detection for overmassive SMBHs due to higher luminosities at a fixed Eddington ratio. However UHZ1's M_•/M_* ratio is still some 1 dex higher than TRINITY AGNs, indicating a discrepancy; (4) TRINITY underpredicts the number densities of GN-z11 and CEERS_1019 analogues. But given the strong constraints from existing data in TRINITY, the extra constraint from GN-z11 and CEERS_1019 does not significantly change TRINITY model results. (5) z = 6-10 quasar luminosity functions will reduce uncertainties in the TRINITY prediction of the z = 6-10 SMBH mass-galaxy mass relation by up to ~0.5 dex. These luminosity functions will be available with future telescopes, such as Roman and Euclid.