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Abstract The evolution of the quasar luminosity function (QLF) is fundamental to understanding the cosmic evolution of black holes (BHs) through their accretion phases. In the era of the James Webb Space Telescope (JWST), Euclid, and Nancy Grace Roman Space Telescope, their unprecedented detection sensitivity and wide survey area can unveil the low-luminosity quasar and low-mass BH population, and provide new insights into quasar host galaxies. We present a theoretical model describing BH growth from initial seeding at z ≳ 20 to ∼ 4, incorporating the duration of accretion episodes, the distribution of Eddington ratios, and the mass dependency of BH accretion rates. By constraining the model parameters with the observed QLFs at 4 ≤ z ≤ 6 across a wide UV luminosity range, we find that the high-redshift BH population grows rapidly at z ≳ 6, and decelerates the pace in subsequent epochs. Toward lower redshifts ( z 10 8 M ⊙ , leading to mass saturation at M • ≳ 10 10 M ⊙ . We predict the BH mass function down to M • ∼ 10 6 M ⊙ for both unobscured and obscured quasar populations at 4 ≤ z ≤ 11, offering a benchmark for future observational tests. Our model accounts for the presence of both bright and faint quasars at z > 4, including those discovered by JWST. Furthermore, our findings suggest two distinct pathways for the early assembly of the BH–galaxy mass correlation: the population with a BH-to-stellar-mass ratio near the local value of M • / M ⋆ ≃ 5 × 10 −3 maintains proximity to the relation via moderate growth, while the population that begins to grow above the local relation becomes as overmassive as M • / M ⋆ ∼ 0.01–0.1 by z ∼ 6 via rapid mass accretion.
Li et al. (Mon,) studied this question.