A two-phase model of galaxy formation: IV. Seeding and growing supermassive black holes in dark matter halos

Yangyao Chen, Houjun Mo, Huiyuan Wang

First listed 2025-09-03 | Last updated 2026-04-25

Abstract

We present a theoretical framework for seeding and growing supermassive black holes (SMBHs) in dark matter halos along their assembly histories. Seeds are bred out of Pop-III stars formed during the first collapse of pristine gas in mini-halos that have reached the $\rm H_2$-cooling limit, modulated by UV radiation from star formation and dynamical heating from fast halo assembly. Such breeding persists until the enrichment of the intergalactic medium (IGM) enables Pop-II stars to form. Post-seeding growth of black holes (BHs) is driven by distinct channels, starting with episodic super-Eddington accretion associated with nuclear bursts induced by global disturbances of galaxies, followed by sustained sub-Eddington accretion via capturing sub-clouds formed in self-gravitating gas clouds (SGCs) in halos of fast assembly, and ending with merger-dominated, quiescent growth. We implement the model in subhalo merger trees to build a coherent framework to follow SMBH-galaxy-halo co-evolution across the whole history and structural hierarchy. BH seeds are bred with a broad mass spectrum of $M_{\rm BH} = 10 - 10^5\,{\rm M}_\odot$ at $z \approx 20 - 30$ in mini-halos with masses of $10^5 - 10^8\,{\rm M}_\odot$. Nuclear bursts provide the key condition for seeds to grow into SMBHs. The $M_{\rm BH}$-$M_*$ relation is a multi-piece, redshift-dependent function shaped by the interplay among different growth channels. Our model predictions are broadly consistent with existing observations; especially, a population of BHs reminiscent of 'little red dots' (LRDs) discovered by JWST naturally results from the seeding and growing processes. Potential future tests of the model are discussed.

Short digest

Builds a seed-to-SMBH pathway inside a two-phase (fast/slow halo growth) framework: Pop III remnants are bred in mini-halos at the H2- (or delayed atomic-) cooling thresholds, then grow via nuclear-burst super-Eddington episodes, SGC sub-cloud capture, and finally mergers. Implemented on subhalo merger trees, the model produces a broad seed spectrum (10–10^5 Msun at z≈20–30) and a multi-piece, redshift-dependent M_BH–M_* relation set by the dominant channel. A key result is that early nuclear bursts enable rapid mass gain, naturally yielding compact accretors reminiscent of JWST little red dots before merger-dominated quiescence. The framework links LW background and halo assembly rate to BH demographics and matches current constraints.

Key figures to inspect

• Figure 1: Use the purple H2-/atomic-cooling and SGC-Jeans bands over halo assembly tracks to read off when/where Pop III collapse and BH seeding occur versus halo mass and growth rate; note how the seeding window shifts with concentration and accretion history.
• Figure 2: Schematic connecting LW radiation and dynamical heating to the Pop III IMF and seed ‘flavors’ (CCSN, PISN, DCBH); trace how increasing delay to atomic-cooling raises the dominant-star mass and yields heavier seeds.
• Figure 3: Collapse-threshold mass versus LW intensity and specific accretion rate, with simulation markers; inspect how the parameterized bands set the seeding delay and move seeds from H2- to atomic-cooling halos—inputs used in the merger-tree implementation.
• Figure 4: Pop III IMFs for different first-star masses and the resulting remnant/seed masses; identify the CCSN–PISN–DCBH transitions that generate the 10–10^5 Msun seed spectrum feeding later growth channels.