Impact of dust cooling on direct-collapse black hole formation

Observations of quasars at z > 6 suggest the presence of black holes with a few times 10⁹ M_⊙. Numerous models have been proposed to explain their existence, including a direct collapse, which provides massive seeds of 10⁵ M_⊙. The isothermal direct collapse requires a strong Lyman-Werner (LW) flux to quench H₂ formation in massive primordial halos. In this study, we explore the impact of trace amounts of metals and dust enrichment. We perform three-dimensional cosmological simulations for two halos of >10⁷ M_⊙ with = 10^-4-10^-6 illuminated by an intense LW flux of J₂₁ = 10⁵. Our results show that initially the collapse proceeds isothermally with T ∼ 8000 K, but dust cooling becomes effective at densities of 10⁸-10¹²cm^-3 and brings the gas temperature down to a few 100-1000 K for Z/Z_⊙ 10^-6. No gravitationally bound clumps are found in the Z/Z_⊙ ≲ 10^-5 cases by the end of our simulations, in contrast to the case with Z/Z_⊙ = 10^-4. Large inflow rates of ≥0.1 M_⊙ yr^-1 are observed for Z/Z_⊙ ≤ 10^-5, similar to a zero-metallicity case, while for Z/Z_⊙=10^-4 the inflow rate starts to decline earlier because of dust cooling and fragmentation. For given large inflow rates, a central star of ∼10⁴ M_⊙ may form for Z/Z_⊙≤10^-5.