Growth of High-Redshift Quasars from Fermion Dark Matter Seeds

TL;DR

The paper addresses how quasars hosting SMBHs with $M_{\rm BH} \gtrsim 10^9\,M_\odot$ at $z>6$ could form from massive seeds without sustained Eddington accretion. It introduces a minimal, cosmology-based growth model where the accretion rate is the minimum of the Bondi inflow and the Eddington limit, with Bondi feeding controlled by a local overdensity factor $f_\rho$ and cosmic gas dilution. Using Bayesian inference on two well-characterized high-redshift quasars, J0313-1806 and J0100+2802, the study finds seed masses $M_0 \sim 10^6\,M_\odot$ formed at $z \sim 20{-}30$ in environments with $f_\rho \gtrsim 50$, producing growth histories featuring an early supply-limited phase, a transitional Bondi-dominated phase, and a late resurgence of near-Eddington accretion. This result aligns with the idea that fermion dark matter cores can produce physically motivated massive seeds and offers a pathway to explain the observed quasar population without invoking persistent Eddington or super-Eddington episodes, with implications for JWST-detectable early seeds and a unified seed-plus-accretion picture for quasars and LRDs.

Abstract

Quasars hosting $\gtrsim 10^{9}\,M_\odot$ black holes at $z>6$ challenge growth scenarios that start from light seeds and assume accretion within already formed galaxies. Motivated by the James Webb Space Telescope (JWST) discovery of Little Red Dots (LRDs), which suggests that $\sim 10^{6}\,M_\odot$ black holes can be active in compact, pre-galactic environments, we revisit early black hole growth with a minimal cosmology-based framework. We model the accretion history as the smaller of the Bondi inflow rate and the Eddington-limited rate, where the Bondi rate is set by the supply of overdense primordial gas whose density declines with cosmic expansion, and the Eddington rate captures regulation by radiative feedback. By fitting the observed masses and luminosities of J0313--1806 ($z=7.64$) and J0100+2802 ($z=6.30$) with Bayesian inference, we infer initial conditions that favor massive seed black holes with initial mass $M_0 \sim 10^{6}\,M_\odot$, formed at $z\sim20{-}30$ in environments with baryonic overdensity factors $f_ρ\gtrsim 50$ relative to the cosmic mean. The resulting growth histories include a prolonged supply-limited stage, and they reproduce the observed quasar masses without requiring sustained Eddington accretion or any super-Eddington episodes. The inferred seed mass scale is consistent with black holes produced by the collapse of quantum-degenerate fermion dark matter cores, providing a physically defined pathway to massive seeds at the redshifts implied by LRD phenomenology.

Figures (4)

• Figure 1: Redshift evolution of the physical mass–energy density of the four standard cosmological components, computed with the Planck 2018 parameters $H_{0}=67.4\;\text{km\,s}^{-1}\text{Mpc}^{-1}$, $\Omega_{\mathrm b}=0.049$, $\Omega_{\mathrm m}=0.315$, $\Omega_{r}=8.4\times10^{-5}$ and $\Omega_{\Lambda}=0.685$. The present-day critical density is $\rho_{\mathrm{crit},0}=8.5\times10^{-30}\,\text{g\,cm}^{-3}$, giving $\rho_{\mathrm b,0}=4.2\times10^{-31}\,\text{g\,cm}^{-3}$, $\rho_{\mathrm m,0}=2.7\times10^{-30}\,\text{g\,cm}^{-3}$, $\rho_{r,0}=7.2\times10^{-34}\,\text{g\,cm}^{-3}$ and $\rho_{\Lambda,0}=5.8\times10^{-30}\,\text{g\,cm}^{-3}$. Densities are followed from $z=10^{4}$ to $z=0.1$ assuming the scalings $\rho\propto(1+z)^{3}$ for baryons and total matter, $\rho\propto(1+z)^{4}$ for radiation, and $\rho=$ constant for dark energy.
• Figure 2: Example showing the Monte Carlo inference of initial conditions for quasar J010013.02+280225.8. growth. The posterior probability distributions of the two key parameters in our model: initial black hole mass (log${10}(M_0/M_\odot) = 5.73^{+0.15}_{-0.15}$) at $z = 1100$ and ambient density enhancement ($\rho/\rho_{\text{b}} = 78.88^{+32.21}_{-23.49}$). Upper panels show marginalized posterior distributions for each parameter. The lower left panel displays the joint probability distribution with 1-$\sigma$ contours, revealing the degeneracy between initial mass and density, a more massive seed can grow in a less dense environment, while a lighter seed requires higher density to reach the observed final mass. The right panel shows the marginalized posterior for the density enhancement, indicating that significant overdensities ($>50$ times cosmic average) are required for efficient early growth.
• Figure 3: Evolutionary history of the quasar in J0313-1806. (a) Black hole mass growth, starting from $9.1^{+4.3}_{-3.6} \times 10^5\, M_\odot$ at $z = 100$ to $1.6 \times 10^9\, M_\odot$ at $z = 7.64$ in a dense environment with $\rho_0 / \rho_{\mathrm{b}} = 77.12^{+47.59}_{-29.99}$. (b) Corresponding luminosity evolution, reaching $1.4 \times 10^{47}$ erg s$^{-1}$. (c) Accretion rate history showing the transition between Bondi-limited (blue) and Eddington-limited (green) regimes, with the actual accretion rate (orange dashed) following the minimum of the two. (d) Eddington ratio $\lambda_{\mathrm{Edd}} = \dot{M}/\dot{M}_{\rm Edd}$ evolution, showing periods of near-Eddington accretion at high redshift, followed by sub-Eddington growth at intermediate redshifts, then rise again at $z\sim 10$. Blue and green shaded regions in all panels represent $1\sigma$ uncertainties derived from the Monte Carlo parameter inference. The probability of black hole seed formation is extremely low at $z > 30$, indicated by the left side of the yellow vertical line.
• Figure 4: Evolutionary history of the quasar J010013.02+280225.8. (a) Black hole mass growth, starting from $8.0^{+2.6}_{-2.1} \times 10^5\, M_\odot$ at $z = 100$ to $1.2 \times 10^{10}\, M_\odot$ at $z = 6.30$ in a dense environment with $\rho_0 / \rho_{\mathrm{b}} = 78.88^{+32.21}_{-23.49}$. (b) Corresponding luminosity evolution, reaching $1.6 \times 10^{48}$ erg s$^{-1}$. (c) Accretion rate history showing the transition between Bondi-limited (blue) and Eddington-limited (green) regimes, with the actual accretion rate (orange dashed) following the minimum of the two. (d) Eddington ratio $\lambda_{\mathrm{Edd}} = \dot{M}/\dot{M}_{\rm Edd}$ evolution, showing periods of near-Eddington accretion at high redshift, followed by sub-Eddington growth at intermediate redshifts, then rise again at $z\sim 10$. Blue and green shaded regions in all panels represent $1\sigma$ uncertainties derived from the Monte Carlo parameter inference. The probability of black hole seed formation is extremely low at $z > 30$, indicated by the left side of the yellow vertical line.