From nuclear star clusters to Little Red Dots: black hole growth, mergers, and tidal disruptions

TL;DR

The paper develops a semi-analytic framework linking nuclear star cluster dynamics, tidal disruption events, and gas accretion to track black hole growth from seeds to the supermassive scale in the early universe. By modeling a two-mass NSC around a central BH and incorporating loss-cone feeding, evaporation, and gas inflows, it predicts elevated rates of TDEs and EMRIs at z ≈ 4–6 and explains why many LRDs appear X-ray faint. It demonstrates that under plausible high-density and gas-rich conditions, IMBH seeds can rapidly reach ≳10^7 M_sun within tens to hundreds of Myr, leaving a detectable multi-messenger footprint (electromagnetic transients and EMRIs) and a potential gravitational-wave background for LISA. The work emphasizes the sensitivity of the results to the NSC properties and gas reservoir, and offers concrete observational tests with JWST, X-ray facilities, and future GW detectors.

Abstract

Little Red Dots, discovered by the James Webb Space Telescope, are hypothesized to be active galactic nuclei containing a supermassive black hole, possibly surrounded by a dense stellar cluster, large amounts of gas, and likely by a population of stellar-mass black holes. We develop a simple nuclear star cluster model to evolve the rapid mass growth of black hole seeds into the supermassive regime. The combined processes of tidal disruption events, black hole captures, and gas accretion are accounted for self-consistently in our model. Given the observed number density of Little Red Dots, and under reasonable assumptions, we predict at least a few tens of tidal disruption events and at least a few black hole captures at $z=4$-$6$, with a tidal disruption event rate an order of magnitude larger than the black hole capture rate. We also estimate the uncertainties in these estimates. Finally, we comment on the low x-ray luminosity of Little Red Dots.

Figures (5)

• Figure 1: Radial profiles of number densities, total enclosed masses, velocity dispersions, and loss-cone and evaporation fluxes. Left: number density of stellar-mass BHs (blue) and stars (red). A massive BH with mass $M_{\rm BH}=10^3\,M_\odot$ is placed in the center of the system. The blue and red vertical dashed lines correspond to the influence radii of BHs and stars, respectively. The inset shows the total mass of BHs (blue) and stars (red) enclosed within radius $r$. The horizontal black dashed line at $M(r)=2M_{\rm BH}$ defines the influence radii. Middle: One-dimensional velocity dispersion for BHs (blue) and stars (red), as well as the escape velocity at radius $r$ (brown dash-dotted). The horizontal black line represents the root-mean-square wandering velocity of the central massive BH. Right: Full and empty loss-cone fluxes of BHs (blue-solid and blue-dashed) and stars (red-solid and red-dashed), as well as the evaporation fluxes of BHs (blue-dotted) and stars (red-dotted). Also shown in the upper right corner are the volume-integrated loss-cone and evaporation fluxes.
• Figure 2: Time evolution of the system shown in Fig. \ref{['fig:initial-snapshot']} with (solid) and without (dashed) gas accretion. In the former scenario, 20 gas inflow episodes, each of $8\cdot10^4\,M_\odot$ of gas, are added uniformly over time. Left: Evolution of the total stellar mass (red), of total mass in stellar-mass BHs (blue), and of the mass of the growing massive BH (black). The vertical green lines correspond to the episodes of gas inflow. Middle: Evolution of the break radii of the stellar (red-solid) and BH (blue-solid) population. Right: Loss-cone (evaporation) rates for stars and BHs are the solid-blue (thin solid-blue) and solid-red (thin solid-red) lines, respectively. The magenta and cyan lines correspond to the 2-body and 3-body stellar-mass binary BH formation rates.
• Figure 3: Left: Cartoon of the spherical cluster model developed in this work. The outer diffuse red region corresponds to the bulk stellar population, and the inner blue overdensity is the subcluster of stellar-mass BH remnants (BHs) in the core surrounding a supermassive BH (SMBH) represented by the central black sphere. The faint green sphere indicates the presence of ionized hydrogen gas in the system. The thin inward (thick outward) arrows show the loss-cone influx (evaporation outflux) of stars $\dot{N}_{\rm lc,1}$ ($\dot{N}_{\rm ev,1}$) and BHs $\dot{N}_{\rm lc,2}$ ($\dot{N}_{\rm ev,2}$). Finally, the green inward and outward green arrows show the influx $\dot{M}_{\rm gas}^{+}$ and outflux $\dot{M}_{\rm gas}^{-}$ of gas from the system, while the inward green arrows $\dot{M}_{\rm BH}^{\rm gas}$ indicate gas accretion into the massive BH. Right: Time evolution of the total stellar mass (red), total mass of stellar-mass BHs (blue), and mass of the massive BH (black). The dashed lines correspond to no gas inflow episodes, while the solid green lines show the gas inflow episodes. The inset shows a linear scale of the massive BH growth and the gas inflow episodes.
• Figure 4: Cumulative number of tidal disruption events (TDEs), captured extreme-mass ratio inspirals (EMRIs), and 2-body binaries (2-body). Left: The cumulative numbers for the simulations of Fig. \ref{['fig:time-evolution']}. The inset shows the rates as a function of time, with the same x-axis as in the main plot. Right: Correspondingly for the simulations of Fig. \ref{['fig:SMBH-growth']}. The cumulative number of 3-body binaries is less than unity in both cases.
• Figure 5: Hard x-rays from the BH hot inner corona scattered on Polish doughnut funnel walls. Funnel model and thick accretion disk are from analytical (left) and numerical simulations (right) Lei:2008ui. Scattering of hard x-rays as depicted for proxy model of Cygnus X-3 2024AA...688L..27V.