Can Supermassive Black Holes Form in Metal-enriched High-Redshift Protogalaxies?

Primordial gas in protogalactic DM halos with virial temperatures T_vir≳ 10⁴ K begins to cool and condense via atomic hydrogen. Provided that this gas is irradiated by a strong UV flux and remains free of H₂ and other molecules, it has been proposed that the halo with T_vir ∼ 10⁴ K may avoid fragmentation and lead to the rapid formation of an SMBH as massive as M ≈ 10⁵–10⁶ M_☉. This "head start" would help explain the presence of SMBHs with inferred masses of several times 10⁹ M_☉, powering the bright quasars discovered in the SDSS at redshift z≳ 6. However, high-redshift DM halos with T_vir ∼ 10⁴ K are likely already enriched with at least trace amounts of metals and dust produced by prior star formation in their progenitors. Here we study the thermal and chemical evolution of low-metallicity gas exposed to extremely strong UV radiation fields. Our results, obtained in one-zone models, suggest that gas fragmentation is inevitable above a critical metallicity, whose value is between Z_cr ≈ 3 × 10⁻⁴ Z_☉ (in the absence of dust) and as low as Z_cr ≈ 5 × 10⁻⁶ Z_☉ (with a dust-to-gas mass ratio of about 0.01Z/Z_☉). We propose that when the metallicity exceeds these critical values, dense clusters of low-mass stars may form at the halo nucleus. Relatively massive stars in such a cluster can then rapidly coalesce into a single more massive object, which may produce an intermediate-mass BH remnant with a mass up to M≲ 10²–10³ M_☉.