Merger-driven buildup of the $M_{\rm BH}$ - $M_*$ relation bridging high-$z$ overmassive black holes with the local relation

Takumi S. Tanaka, John D. Silverman, Kazuhiro Shimasaku, Knud Jahnke, Junyao Li, Makoto Ando

First listed 2026-03-12 | Last updated 2026-04-09

Abstract

The origin of the mass scaling relation between supermassive black holes (SMBHs, $M_{\rm BH}$) and galaxies ($M_*$) remains a key open question. Rather than invoking AGN feedback, a non-causal mechanism has been proposed in which multiple mergers average out the $M_{\rm BH}/M_*$ ratio, thus decreasing its scatter ($σ$) and forming a tight local mass relation over cosmic history. A larger scatter in the relation at higher redshift suggested from a non-causal evolutionary scenario may be evident from recent JWST observations of overmassive SMBHs at high redshift. Here, we carry out a Monte Carlo simulation of solely merger-induced evolution of galaxies and their SMBHs which incorporates recent high-redshift observational constraints on $σ$ and the galaxy merger rate. We find that the dispersion in the local mass relation can be reproduced, even when starting from a highly scattered population at $z\sim6$ with $σ=0.8\,{\rm dex}$ or $1.0\,{\rm dex}$, which are in agreement with recent JWST studies. The redshift evolution of the scatter is highly sensitive to the mass ratio between merging pairs and the merger rate, and minor mergers with higher frequency than major mergers can also contribute to the scatter evolution, highlighting the importance of accurately constraining these parameters at high redshift through observations. Furthermore, statistical surveys aimed at determining the $M_*$-dependence of $σ$ and constraining $σ$ at $z\sim3-4$ will be effective in testing this scenario.

Short digest

Monte Carlo merger-only experiments evolve the MBH–M* plane from z≈6 to 0 using observed high‑z scatter and redshift‑dependent merger rates. The models reproduce the local dispersion (~0.3 dex) even when initialized with σ=0.8–1.0 dex at z≈6, and they show that the decline of scatter is highly sensitive to the mass‑ratio distribution and overall merger frequency, with frequent minor mergers also accelerating convergence. This provides a non‑causal “averaging” bridge between JWST reports of overmassive SMBHs and the local relation. The authors highlight that measuring the M*‑dependence of σ and securing σ at z≈3–4 will be decisive tests.

Key figures to inspect

• Evolution of σ(z) for different merger‑rate prescriptions and mass‑ratio cuts; verify that tracks starting at σ=0.8/1.0 converge to ~0.3 by z≈0 and how minor‑merger–dominated histories differ from major‑only cases.
• MBH–M* distributions at z≈6, z≈3–4, and z≈0 (scatter contours/residuals); inspect how the high‑σ initial population tightens and whether an overmassive tail persists at intermediate redshift.
• Predicted σ versus M* (mass‑dependent scatter) at z≈3–4; identify the mass bins where deviations are largest to target with upcoming surveys.
• Cumulative number of mergers per galaxy versus redshift, split into major and minor; assess the central‑limit averaging behavior and quantify the relative contribution of minor mergers.
• Sensitivity test comparing alternative galaxy‑replenishment strategies or merger‑rate parameterizations; check robustness of σ(z) convergence against these choices.