Heavy Seed Black Hole Growth in Metal-Enriched Halos through Disk-Induced Stellar Disruptions: A Semi-Analytical Modelling

Recent simulations suggest that heavy seed black holes may form in weakly metal-enriched atomic cooling halos, where the supermassive-star progenitor and small-scale stellar fragments emerge nearly coevally. In this picture, the newly born heavy seed is naturally embedded in a metal-enriched Pop I/II nuclear star cluster rather than in an isolated pristine environment. We investigate whether disk-induced tidal disruption events (TDEs) from these Pop I/II stars can provide an efficient and sustained growth channel for heavy seed black holes. We construct a semi-analytical model for stellar orbital damping, disk capture, migration, and tidal disruption around a heavy seed black hole, and incorporate the resulting disk-induced TDE contribution into cosmological merger trees with baryonic and metallicity evolution. Heavy seed host halos are selected from atomic cooling halos with Z 10-3Z that satisfy either a rapid gas-inflow criterion or a strong Lyman--Werner radiation criterion. We find that disk-induced Pop I/II TDEs can dominate the early growth of heavy seeds: the median black hole mass grows from about10 4,M to about10 5,M within the first about0.1 Gyr after seed formation, and reaches several 10 5,M by about0.2 Gyr. The cumulative mass supplied by TDEs initially exceeds that from gas accretion and remains comparable over the first about200 Myr. Including disk-induced TDEs shifts the black hole population toward higher masses, increases the abundance of massive black holes at z about9 --10, and produces larger black hole-to-stellar mass ratios. This channel helps alleviate, but does not fully remove, the tension between heavy-seed models and the most extreme high-redshift black hole candidates, suggesting that additional growth mechanisms may still be required.