Evolution of High-redshift Quasar Hosts and Promotion of Massive Black Hole Seed Formation

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.