Early results of James Webb Space Telescope observations have delivered bright z ≳ 10 galaxy candidates in greater numbers than expected, enabling construction of rest-frame UV luminosity functions (LFs). The LFs contain key information on the galaxy assembly history, star formation activity, and stellar population of the distant universe. Given an upper bound of the total baryonic mass inflow rate to galaxies from their parent halos estimated from abundance matching, we derive a lower bound on the product of the star formation and UV photon production efficiency in galaxies at each redshift. This stringent constraint requires a high efficiency (≳10%–30%) converting gas into stars, assuming a normal stellar population with a Salpeter-like mass distribution. The efficiency is substantially higher than those of typical nearby galaxies, but is consistent with those seen in starburst galaxies and super-star clusters observed in the nearby universe. Alternatively, the star formation efficiency may be as low as a few percent, which is the average value for the entire galaxy population at z ≃ 6, if the stellar population is metal-free and drawn from a top-heavy mass distribution that produces more intense UV radiation. We discuss several other possible scenarios to achieve the constraint, for instance, energetic radiation produced from compact stellar remnants and quasars, and propose ways to distinguish the scenarios by forthcoming observations.

High-redshift luminous quasars powered by accreting supermassive black holes (SMBHs) with mass ≳109 M ⊙ constrain their formation pathways. We investigate the formation of heavy seeds of SMBHs through gas collapse in the quasar host progenitors, using merger trees to trace the halo growth in highly biased, overdense regions of the universe. The progenitor halos are likely irradiated by intense H2-photodissociating radiation from nearby star-forming galaxies and heat the interior gas by successive mergers. The kinetic energy of the gas originating from mergers, as well as the baryonic streaming motion, prevents gas collapse and delays prior star formation. With a streaming velocity higher than the rms value, gas clouds in nearly all 104 realizations of merger trees enter the atomic-cooling stage and begin to collapse isothermally with T ≃ 8000 K via Lyα cooling. The fraction of trees that host isothermal gas collapse is 14% and increases with streaming velocity, while the rest form H2-cooled cores after short isothermal phases. If the collapsing gas is enriched to Z crit ∼ 2 × 10−3 Z ⊙, requiring efficient metal mixing, this fraction could be reduced by additional cooling via metal fine-structure lines. In the massive collapsing gas, the accretion rate onto a newly born protostar ranges between 3 × 10−3 M ⊙ yr−1 and 5 M ⊙ yr−1, among which a large fraction exceeds the critical rate suppressing stellar radiative feedback. As a result, we expect a distribution of stellar mass (presumably BH mass) ranging from several hundred to above 105 M ⊙, potentially forming massive BH binary mergers and yielding gravitational-wave events.

The early evolution of the quasar luminosity function (QLF) and black hole mass function (BHMF) encodes key information on the physics determining the radiative and accretion processes of supermassive black holes (BHs) in high-z quasars. Although the QLF shape has been constrained by recent observations, it remains challenging to develop a theoretical model that explains its redshift evolution associated with BH growth self-consistently. In this study, based on a semianalytical model for the BH formation and growth, we construct the QLF and BHMF of the early BH population that experiences multiple accretion bursts, in each of which a constant Eddington ratio is assigned following a Schechter distribution function. Our best-fit model to reproduce the observed QLF and BHMF at z ≃ 6 suggests that several episodes of moderate super-Eddington accretion occur and each of them lasts for τ ≃ 20–30 Myr. The average duty cycle in super-Eddington phases is ≃15% for massive BHs that reach ≳108 M ⊙ by z ≃ 6, which is nearly twice that of the entire population. We find that the observed Eddington ratio distribution function is skewed to a lognormal shape owing to detection limits of quasar surveys. The predicted redshift evolution of the QLF and BHMF suggests a rapid decay of their number and mass density in a cosmic volume toward z ≳ 6. These results will be unveiled by future deep and wide surveys with the James Webb Space Telescope, Roman Space Telescope, and Euclid.