A Unified Dark-matter-driven Relativistic Bondi Route to Black Hole Growth from Stellar to Supermassive Scales

Observations of luminous quasars at z ≳ 7 reveal supermassive black holes (SMBHs) with inferred masses M_BH ∼ 10⁹ M_⊙ formed within the first ∼700 Myr of cosmic history. Standard growth channels—Eddington-limited gas accretion and hierarchical mergers—face severe timescale restrictions. We consider a super-Eddington accretion mechanism aided by the Bondi accretion of a minimal model of self-interacting dark matter (SIDM). We demonstrate that in a critical regime with a near-relativistic sound speed, Bondi accretion yields an accretion rate that depends only on the SIDM mass m, thus it is universal across the ambient environment. This critical accretion mechanism for m ≳ 10⁻² eV can grow seeds as small as 10 M_⊙ primordial black holes (PBHs) in the early Universe into 10⁹–10¹⁰ M_⊙ SMBHs by z ∼ 7 without fine-tuned environments. Therefore, given a mass distribution of PBHs and a value of m, the mass function of primary black holes at late time can be fully determined with masses ranging from stellar to SMBHs. This connects the microscopic physics of dark matter to astrophysical observations of black holes.