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 $\gtrsim 10^9 M_\odot$ 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 H$_2$-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 baryonic streaming motion prevents gas collapse and delays prior star formation. With a streaming velocity higher than the root-mean-square value, gas clouds in nearly all $10^4$ realizations of merger trees enter the atomic-cooling stage and begin to collapse isothermally with $T \simeq 8000 K$ via Ly$\alpha$ cooling. The fraction of trees which host isothermal gas collapse is $14\%$ and increases with streaming velocity, while the rest form H$_2$-cooled cores after short isothermal phases. If the collapsing gas is enriched to $Z_{crit}\sim 2\times 10^{-3} Z_\odot$, 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 $3 \times 10^{-3}-5 M_\odot yr^{-1}$, 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 $10^5 M_\odot$, potentially forming massive BH binary mergers and yielding gravitational wave events.