A Unified Dark-Matter--Driven Relativistic Bondi Route to Black-Hole Growth from Stellar to Supermassive Scales

Abstract

Observations of luminous quasars at $z\gtrsim7$ reveal supermassive black holes (SMBHs) with inferred masses $M_{\rm BH}\sim10^9 \, M_\odot$ formed within the first $\sim700$~Myr of cosmic history. Standard growth channels \textrm{ -- } Eddington-limited gas accretion and hierarchical mergers \textrm{ -- } 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 {\it critical regime} with a near-relativistic sound speed, the Bondi accretion yields an accretion rate that depends only on the mass $m$ of SIDM, thus it is universal to the ambient environment. This critical accretion mechanism for $m\gtrsim 10^{-2}\; {\rm eV}$ can grow seeds as small as $10\,M_\odot$ primordial black holes (PBH) in the early Universe into $10^9$ \textrm{--} $10^{10}\,M_\odot$ SMBHs by $z\sim7$ 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.