Black Hole merger rates in the first billion years in light of JWST data

Context. Recent James Webb Space Telescope (JWST) discoveries have unveiled an abundance of faint and massive Active Galactic Nuclei (AGNs) at high redshifts (z=4-9), that surpass by 10 to 100 times the extrapolated bolometric (Bol) and ultraviolet (UV) luminosity functions (LF) from previous AGN campaigns. The two main models that are put forward to explain these observations correspond to light seeds (150 Msol) accreting in episodes of super Eddington, and heavy seeds ($10^3$ - $10^5$ Msol) growing at the Eddington limit. Future gravitational observatories like the Laser Interferometer Satellite Antenna (LISA) will help disentangle these models by reporting the BH-BH merger events from mid to high redshifts. Aims. This work aims to report the predicted merger rates in the heavy seed scenario in light of recent JWST data. In our models we explore (i) instantaneous merging between BHs, (ii) delayed merging after a dynamical timescale, as well as extreme spin configurations (a=0.99, a=-0.99) to bracket BH mass growth. Methods. We use Delphi, a semi-analytical model that tracks baryonic physics over a hierarchical evolution of dark matter halos through cosmic time within the first billion years of the Universe. We calibrate this model for it to simultaneously reproduce galaxy and JWST-AGNs observables. Results. We show reasonable agreement with the Bolometric Luminosity function at z=6, where BHs must accrete 10-100 times more gas than in previous works calibrated to pre-JWST data. However, we underpredict (overpredict) the bright end $10^45.5$ erg s$^-1$ (all luminosity range) at z=7 (z=5) by 1-3.2 dex (0.22-1.6 dex). Regarding BH-BH merger events, the instantaneous (delayed) models predict a total of 28.06 (19.61) yr$^-1$ for BHs at z>=5, which is within the range of merger rates reported in previous literature.

💡 Research Summary

This paper investigates the predicted black‑hole (BH) merger rates during the first billion years of cosmic history, focusing on the “heavy‑seed” scenario in light of the unprecedented active‑galactic‑nucleus (AGN) populations uncovered by the James Webb Space Telescope (JWST). Recent JWST observations have revealed a number density of faint and luminous AGN at redshifts z ≈ 4–9 that exceeds pre‑JWST extrapolations of the bolometric and ultraviolet luminosity functions by one to two orders of magnitude. Such an excess challenges existing models of early super‑massive black‑hole (SMBH) growth and motivates a reassessment of merger predictions that were previously calibrated on older data sets.

The authors employ Delphi, a semi‑analytical model (SAM) that follows the hierarchical assembly of dark‑matter halos from z ≈ 26 down to z ≈ 4.5, tracking the coupled evolution of gas, stars, metals, dust, and BHs. Dark‑matter merger trees are generated with the Parkinson et al. (2007) algorithm, using a mass resolution of 10⁸ M⊙ and a fixed timestep of 30 Myr. Gas accretion onto halos follows the cosmological baryon‑to‑dark‑matter ratio, while star formation rates are derived from cold‑gas fractions and star‑formation efficiencies calibrated on the Sphinx‑20 hydrodynamic simulation. UV luminosities are computed with Starburst99, and dust attenuation is applied via an optical‑depth prescription.

Heavy BH seeds (10³–10⁵ M⊙) are planted in all metal‑free halos down to z ≈ 12.8, with masses drawn from a log‑uniform distribution. BH growth proceeds under two competing limits: (i) a fraction of the Eddington accretion rate (f_Edd) and (ii) a fraction of the remaining gas after supernova feedback (f_BH,acc). Both parameters are allowed to scatter log‑normally with σ = 0.5 dex and adopt higher values once the host halo exceeds a critical mass M_crit ≈ 10¹¹·²⁵ M⊙, reflecting the expectation that massive halos can retain gas in their centers despite stellar feedback. Radiative efficiency ε_r(a) depends on the BH spin a, with extreme prograde (a = +0.99) and retrograde (a = ‑0.99) cases explored to bracket uncertainties in mass‑to‑energy conversion. Accretion episodes with effective Eddington ratios below 1 % are treated as radiatively inefficient flows (RIAFs) and assumed to be non‑luminous.

Two merger prescriptions are investigated. In the “instantaneous” model, BHs merge as soon as their host halos coalesce. In the “delayed” model, a dynamical‑timescale delay (≈30 Myr) is imposed before the BHs combine, mimicking the time required for binary hardening and gravitational‑wave inspiral. For each scenario, the authors compute the evolving BH mass function, bolometric luminosity function, and the resulting gravitational‑wave event rate observable by future detectors such as LISA.

Model calibration is performed simultaneously against JWST‑derived AGN number densities, the bolometric luminosity function at z = 6, and the stellar‑to‑BH mass relation inferred from early galaxies. The calibrated model reproduces the observed bolometric LF at z = 6 only if BHs accrete 10–100 times more gas than required in pre‑JWST models, implying either sustained near‑Eddington accretion or highly efficient gas inflows. Nevertheless, the model underpredicts the bright‑end (L ≈ 10⁴⁵·⁵ erg s⁻¹) at z = 7 by 1–3.2 dex and overpredicts the full luminosity range at z = 5 by 0.22–1.6 dex, highlighting residual tensions.

The predicted merger rates are 28.06 yr⁻¹ for the instantaneous case and 19.61 yr⁻¹ for the delayed case, both for events with z ≥ 5. These values sit comfortably within the broad range reported in earlier theoretical works (0.02–244 yr⁻¹ for heavy seeds, 26–140 yr⁻¹ for light seeds). The authors argue that, despite the uncertainties in spin distribution, feedback efficiencies, and possible JWST selection biases, the heavy‑seed pathway can naturally produce a substantial high‑redshift merger population that will be accessible to LISA.

In the discussion, the paper emphasizes the need for (a) better constraints on BH spin evolution, (b) refined modeling of supernova‑driven outflows and gas recycling, and (c) a careful assessment of JWST AGN sample completeness. The authors conclude that forthcoming gravitational‑wave observations will be decisive in discriminating between light‑ and heavy‑seed formation channels, and that their JWST‑calibrated SAM provides a robust framework for interpreting those future data.