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

TL;DR

This work proposes a unified, dark-matter–driven channel for rapid black-hole growth by leveraging a relativistic self-interacting DM fluid ($\phi^4$-SIDM) in a critical Bondi accretion regime. In the limit $a_s^2\to 1/9$, the Bondi rate becomes $\dot{M}_{\rm Bondi}=64\pi\rho_B M^2$ with $\rho_B=\frac{3m^4}{2\lambda}$, making the growth largely independent of the ambient halo environment and controlled by the microscopic SIDM mass $m$. The authors derive an analytic growth law under simultaneous Eddington accretion, show a transition mass $M_*=\Gamma/K\propto m^{-5/2}$ that marks when Bondi inflow dominates, and apply the solution to PBH seeds from the QCD epoch to predict the high-redshift SMBH mass function by $z=7$. Their results establish a falsifiable link between DM microphysics and SMBH demographics, predicting distinctive features in the PBH mass function and offering a new pathway to explain luminous quasars at $z\gtrsim 7$.

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.

Figures (4)

• Figure 1: Mass evolution of a $10\,M_\odot$ seeding black hole from $z=30$ to $z=7$, including Eddington accretion and relativistic SIDM Bondi inflow. Shown are four representative SIDM masses, $m=1,~10^{-1}, 10^{-2}$, and $10^{-3}$ eV, evolved in a Press--Schechter median halo enhanced by an order of magnitude with a total SIDM supply fraction $f_{\rm halo}=0.9$. The heavier SIDM reaches the transition mass $M_\star$ (marked by crosses) earlier and experiences a rapid growth phase until saturating at the finite halo supply. In comparison, the lighter SIDM remains and experiences rapid growth at a later period.
• Figure 2: Counterpart evolution of the Bondi radius $r_B(z)$ of Fig. \ref{['fig:PBHGrowth']}, assuming the average-halo density of (\ref{['rho_DM_z']}). The $y$-axis is in parsecs (logarithmic), while the $x$-axis is linear in redshift from $z=30$ (left) to $z=7$. This demonstrates how the Bondi radius expands across cosmic epochs, eventually approaching or crossing the inner-halo scale (represented by the dashed line). This enables efficient SIDM feeding in the late growth phase to form SMBHs with masses $\geq 10^9 M_\odot$ if the crossing occurs at $z > 7$.
• Figure 3: Evolution of the QCD PBH mass function for Log-normal(top), power-law (middle), and critical-collapse (down) distributions to $z=7$ under SIDM-Bondi-aided Eddington accretion with DM mass $m=10^{-3,-2,-1} \; {\rm eV}$. The growth triggers early Bondi dominance for $m\gtrsim 10^{-2} \; {\rm eV}$ to reach $10^{10} M_\odot$ SMBHs. The insets in each figure show the finer structures of the final mass function.
• Figure S1: Mass-Radius relation for the TOV configurations of $\phi^4$-SIDM with $\rho_B=10^{-4} \rho_\odot$.