Rapid sinking and efficient mergers of supermassive black holes in compact high-redshift galaxies

We present a cosmological zoom-in simulation targeting the high redshift compact progenitor phase of massive galaxies, with the most massive galaxy reaching a stellar mass of $M_{\star}=8.5\times 10^{10} \ M_{\odot}$ at $z=5$. The dynamics of supermassive black holes (SMBHs) is modelled from seeding down to their coalescence at sub-parsec scales due to gravitational wave (GW) emission by utilising a new version of the KETJU code, which combines regularised integration of sufficiently massive SMBHs with a dynamical friction subgrid model for lower-mass SMBHs. All nine massive galaxies included in this study go through a gas-dominated phase of early compaction in the redshift range of $z\sim 7-9$, starting at stellar masses of $M_\star\gtrsim 10^8\ \mathrm{M}\odot$ and ending at a few times $M{\star}\sim 10^9\ \mathrm{M}\odot$. The sizes, masses and broad band fluxes of these compact systems are in general agreement with the population of systems observed with JWST known as `Little Red Dots’. In the compact phase, the stellar and SMBH masses grow rapidly, leading to a sharp decline in the central gas fractions. The outer regions, however, remain relatively gas-rich, leading to subsequent off-centre star formation and size growth. Due to the very high central stellar densities ($ρ{\star}\gtrsim 10^{13},\mathrm{M_\odot/kpc^3}$), the SMBHs merge rapidly, typically just $\sim 4-35\ \mathrm{Myr}$ after the SMBH binaries have become bound. Combining KETJU with the phenomenological PhenomD model resolves the complete evolution of the GW emission from SMBH binaries through the Pulsar Timing Array frequency waveband up to the final few orbits that produce GWs observable with the future LISA mission.

💡 Research Summary

This paper presents a state‑of‑the‑art cosmological zoom‑in study of the compact, high‑redshift galaxy population recently identified by JWST as “Little Red Dots” (LRDs). The authors develop a new version of the KETJU code that couples the regularised mSTAR integrator (which resolves black‑hole–black‑hole and black‑hole–star interactions without gravitational softening) with a sub‑grid dynamical‑friction model for low‑mass seed black holes. This hybrid approach eliminates the need for artificial repositioning, allows seed black holes to experience realistic drag from surrounding stars and dark matter, and enables the simulation to follow SMBH dynamics from the seeding stage (∼10⁵–10⁶ M⊙) down to sub‑parsec separations where gravitational‑wave (GW) emission dominates.

The code is validated using idealised Plummer and Hernquist spheres, showing that the dynamical‑friction prescription reproduces the sinking timescales of low‑mass black holes and correctly captures Brownian motion, while the regularised region reproduces the high‑accuracy dynamics of massive binaries.

In the main cosmological runs, nine massive galaxies are followed from z≈9 to z≈5. All experience an early, gas‑dominated compaction episode between z≈7–9, growing from M★≈10⁸ M⊙ to a few ×10⁹ M⊙ while shrinking to radii ≲1 kpc. The central stellar densities reach ρ★≳10¹³ M⊙ kpc⁻³, and the gas fraction in the core drops sharply, whereas the outskirts remain gas‑rich, fueling off‑centre star formation and subsequent size growth.

During this compact phase, SMBHs grow rapidly through accretion and mergers, reaching masses of 10⁸–10⁹ M⊙. The high stellar density and low central gas content produce very efficient dynamical friction and three‑body scattering, so that once a binary becomes bound it hardens to separations of ∼1–10 pc and then shrinks to sub‑parsec scales within 4–35 Myr. The authors include post‑Newtonian corrections up to 3.5PN and use the phenomenological PhenomD waveform model to follow the GW signal continuously from the nanohertz band (relevant for Pulsar Timing Arrays) through the millihertz band (targeted by LISA). The predicted stochastic GW background matches current PTA hints, and the individual chirp signals are strong enough to be detectable by LISA out to very high redshifts.

Comparisons with JWST observations show that the simulated galaxies reproduce the sizes, stellar masses, and broadband colours of the observed LRDs, and the simulated dual‑AGN fraction aligns with the unexpectedly high dual‑AGN rates reported at z > 6.

The study highlights three major implications: (1) the extreme central densities of compact high‑z galaxies naturally solve the “final‑parsec problem” without invoking exotic gas discs or massive stellar cores; (2) the sub‑grid dynamical‑friction model allows physically realistic early SMBH growth from low‑mass seeds; (3) high‑z SMBH mergers constitute a joint source for both PTA‑scale stochastic backgrounds and LISA‑scale resolvable events, providing a direct bridge between electromagnetic and gravitational‑wave observations of the early Universe.

Limitations include the still modest mass resolution for gas and stars, simplified AGN feedback prescriptions, and the neglect of possible circumbinary disc torques. Future work will aim at higher resolution, more sophisticated feedback, and a statistical exploration of SMBH‑galaxy co‑evolution across a larger cosmological volume. In summary, the new KETJU‑DF framework delivers the first self‑consistent, high‑resolution simulation of SMBH formation, rapid sinking, and efficient merger in compact high‑redshift galaxies, offering testable predictions for JWST, PTA, and LISA observations.