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arxiv: 2508.11846 · v3 · submitted 2025-08-15 · 🌌 astro-ph.HE · hep-ph

Dark Matter and the Early Formation of Supermassive Black Holes

Andrew Imai , Grant J. Mathews , Guobao Tang , Brian Zhang This is my paper

Pith reviewed 2026-05-18 22:06 UTC · model grok-4.3

classification 🌌 astro-ph.HE hep-ph
keywords supermassive black holeshigh redshiftdark matter capturenuclear star clustersultralight dark matterblack hole growthearly universe
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The pith

Clustered dark matter allows small black hole seeds to reach over 10 million solar masses by redshift 10 in nuclear star clusters.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how supermassive black holes form at very high redshifts through a mix of dark matter capture, mergers, and gas accretion inside dense nuclear star clusters. Standard models drawn from galaxy formation simulations show that dark matter in the usual NFW distribution adds almost nothing to the growth. Yet the authors identify scenarios where dark matter clusters more strongly, possibly via self-interactions, and demonstrate that this clustering lets a stellar-remnant seed black hole grow rapidly. The same conclusion holds for both ordinary cold dark matter and ultralight dark matter of mass near 10 to the minus 22 electron volts. Explaining the earliest supermassive black holes matters because it reduces reliance on extreme gas accretion rates or other special conditions at early times.

Core claim

In models where dark matter clustering occurs, possibly by self-interaction, the capture of dark matter by a growing supermassive black hole allows a small seed stellar-remnant black hole to reach more than 10^7 solar masses by redshift 10 in the core of dense nuclear star clusters. This remains true for either cold dark matter or ultralight dark matter with mass around 10^{-22} eV. In contrast, when the dark matter follows the standard NFW profile from cosmological simulations, its contribution to black hole growth is insignificant.

What carries the argument

Capture of collisionless dark matter by the growing black hole when the dark matter is allowed to cluster beyond the standard NFW profile inside nuclear star clusters.

If this is right

  • A stellar-remnant seed black hole can reach supermassive size by redshift 10 even when gas accretion and mergers are limited to Eddington rates and tidal disruption events.
  • The dark matter contribution becomes important only when clustering occurs beyond what standard cosmological simulations produce.
  • The same growth pathway works for ultralight dark matter, where the de Broglie wavelength exceeds the initial size of the nuclear star cluster and produces distinct capture behavior.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If self-interacting dark matter is required to explain early black hole growth, it could also alter predictions for galaxy core densities and satellite galaxy counts at lower redshifts.
  • Future observations of black hole masses and host galaxy properties at redshift 10 could distinguish between clustered and standard dark matter profiles.

Load-bearing premise

Dark matter can cluster enough, possibly through self-interactions, for the growing black hole to capture a significant amount of it.

What would settle it

A direct measurement of the dark matter density profile in the centers of galaxies at redshift around 10 that closely follows the NFW shape with no extra central clustering would show the dark matter contribution remains negligible.

Figures

Figures reproduced from arXiv: 2508.11846 by Andrew Imai, Brian Zhang, Grant J. Mathews, Guobao Tang.

Figure 1
Figure 1. Figure 1: Radial density profiles at redshift z ≈ 20 of dark matter (blue points) and total baryonic matter (or￾ange points) extracted from the inner 200 pc of a galaxy that contains a 6 × 108 M⊙ SMBH at z = 0 within TNG50 simulation. The solid (DM) and dashed (baryon) lines rep￾resent the best-fitting Navarro–Frenk–White (NFW) profiles to each component. 10 3 10 2 10 1 10 0 10 1 Radius [pc] 10 5 10 3 10 1 10 1 10 3… view at source ↗
Figure 2
Figure 2. Figure 2: Soliton profile for scalar field of mass µs = 10−20 eV associated with a model with a cluster half-mass radius of 0.50 pc. mass of 8×108 M⊙ (Turner 1991). For baryonic matter, we took the initial star-to-gas mass ratio to be 4:1. We simulate clusters with initial half-mass radii of varying sizes (0.1, 0.2, 0.5, and 1.0 pc). These initial radii are somewhat larger than those adopted by Kritos et al. (2024b)… view at source ↗
Figure 3
Figure 3. Figure 3: shows that the most dense cluster with an initial virial half-mass radius of 0.10 parsecs attains an SMBH of ∼ 3 × 107 M⊙ within 200 Myr, nearly ac￾counting for the observation (Natarajan et al. 2024) of an SMBH of 4 × 107 M⊙ at z = 10 and easily explain￾ing the presence of an SMBH of mass 1.5 × 107 M⊙ in a near-pristine galaxy at z = 7.04 as described by Maiolino et al. (2025). In contrast, the simulation… view at source ↗
Figure 4
Figure 4. Figure 4: SMBH growth in models with varying DM– to-baryon ratios while maintaining a constant baryon cluster mass. Other parameters are the same as in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: Models with various masses µs for the scalar field ultralight DM. The initial conditions are the same as in [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: Growth of the half-mass radius of the NSC with various values for the ULDM mass and rh = 0.2 pc. 4. CONCLUSIONS In summary, we have studied the role of DM in the early growth of a seed stellar black hole into an SMBH in a dense nuclear cluster. We find that with the inclusion of CDM (or ULDM with mass µs ∼ 10−20 eV), a central seed black hole can more easily grow to the 4 × 107 M⊙ SMBH detected at z = 10 b… view at source ↗
Figure 8
Figure 8. Figure 8: Evolution of SMBH mass (top panel), ULDM density (middle panel) and rate of SMBH growth (bottom panel) for a model with 10−20 eV ULDM mass and an initial core radius of 0.2 pc. ACKNOWLEDGEMENTS Work at the University of Notre Dame is supported by the U.S. Department of Energy under Nuclear The￾ory Grant DE-FG02-95-ER40934. We acknowledge sup￾port from the University of Notre Dame Center for Re￾search Compu… view at source ↗
read the original abstract

We investigate the growth of supermassive black holes (SMBHs) at high redshift ($z \ge 10$) from a combination of dark matter capture, black-hole mergers, and gas accretion. It has previously been shown that SMBHs can form by $z \approx 10$ via black-hole mergers, Eddington-limited Bondi gas accretion and tidal disruption events with stars within dense nuclear clusters. Here, we examine the degree to which the capture of collisionless dark matter by a growing SMBH may also contribute. We first consider models deduced from cosmological simulations of galaxy formation and central BH formation. We show that in the case that the dense nuclear star cluster forms by cooling and collapse of gas, while the DM remains in a standard NFW profile, the contribution from cold dark matter accretion is insignificant. However, we suggest models for which dark matter clustering can occur (possibly by self interaction). We show that such clustering may affect SMBH growth. In such cases, a small seed stellar-remnant black hole can more easily reach $> 10^7$ M$_{\odot}$ by $z = 10$ in the core of dense nuclear star clusters. This remains true for either cold dark matter or ultralight dark matter with the observationally inferred mass of $\sim 10^{-22}$ eV. We highlight the unique possible evolution of ULDM capture by the growing SMBH due to the fact that the ULDM de Broglie wavelength exceeds the initial nuclear star cluster half-mass radius.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates the contribution of dark matter capture to the growth of supermassive black holes at high redshifts (z ≥ 10) within dense nuclear star clusters, in conjunction with black hole mergers and gas accretion. It concludes that while standard Navarro-Frenk-White (NFW) dark matter profiles yield insignificant contributions, proposed models allowing for dark matter clustering (possibly through self-interactions) enable stellar-remnant seed black holes to reach masses exceeding 10^7 solar masses by z=10. This result is asserted to apply to both cold dark matter and ultralight dark matter with masses around 10^{-22} eV, noting unique aspects of ULDM capture due to its de Broglie wavelength surpassing the nuclear star cluster half-mass radius.

Significance. Should the clustering scenarios prove physically realizable, the paper offers a potential additional pathway for explaining the existence of massive black holes at early cosmic times, complementing existing models based on mergers and accretion. The discussion of ultralight dark matter introduces an interesting distinction in capture dynamics that could be explored further in future work.

major comments (2)
  1. [Abstract] Abstract: The central claim that growth to >10^7 M⊙ by z=10 'remains true' for ULDM with m∼10^{-22} eV is not supported by any quantitative capture-rate estimates or density-profile calculations; the noted de Broglie wavelength exceeding the NSC half-mass radius is highlighted but not shown to permit (rather than suppress) net capture relative to the clustered CDM case.
  2. [Clustering models] Clustering models: The suggestion that dark matter clustering 'can occur (possibly by self interaction)' is introduced as an ad-hoc modeling choice without derivation, simulation outputs, or specific density-enhancement factors; this assumption is load-bearing for the claim that DM capture becomes significant enough to ease SMBH growth beyond the NFW case.
minor comments (1)
  1. [Abstract] Abstract: Add citations to the specific cosmological simulations used to establish the 'insignificant' NFW contribution for direct comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and indicate the revisions we will make to strengthen the presentation and support for our claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that growth to >10^7 M⊙ by z=10 'remains true' for ULDM with m∼10^{-22} eV is not supported by any quantitative capture-rate estimates or density-profile calculations; the noted de Broglie wavelength exceeding the NSC half-mass radius is highlighted but not shown to permit (rather than suppress) net capture relative to the clustered CDM case.

    Authors: We agree that the ULDM discussion in the current manuscript is qualitative. The text notes the de Broglie wavelength exceeding the initial NSC half-mass radius as leading to a unique possible evolution for capture, distinct from point-particle CDM. This is intended to indicate that wave-like behavior in a clustered environment does not suppress but permits net capture sufficient for the growth claim to hold. To address the concern, we will revise the abstract for precision and add a short quantitative discussion in the main text, including order-of-magnitude capture-rate estimates based on the wave nature of ULDM relative to the clustered CDM case. revision: yes

  2. Referee: [Clustering models] Clustering models: The suggestion that dark matter clustering 'can occur (possibly by self interaction)' is introduced as an ad-hoc modeling choice without derivation, simulation outputs, or specific density-enhancement factors; this assumption is load-bearing for the claim that DM capture becomes significant enough to ease SMBH growth beyond the NFW case.

    Authors: The clustering scenarios are presented as motivated suggestions rather than results derived within this work. We note that self-interacting dark matter has been proposed in the literature to produce denser central profiles than NFW. We will expand the relevant section to include specific references to SIDM studies, state the density-enhancement factors adopted in our calculations, and clarify that these models are exploratory to illustrate the potential impact of clustering on SMBH growth. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper begins from external cosmological simulation models to establish baseline NFW profiles, explicitly notes that these yield insignificant DM capture, then conditionally explores suggested clustering scenarios (possibly via self-interaction) as alternative inputs. The resulting growth statements to >10^7 M⊙ by z=10 are presented as outcomes under those alternative assumptions rather than predictions derived from or equivalent to the inputs themselves. The ULDM section highlights a qualitative difference arising from the de Broglie wavelength exceeding the NSC half-mass radius but does not reduce any capture-rate equation to a self-defined or fitted parameter that forces the conclusion. No self-citation load-bearing steps, uniqueness theorems, or ansatzes imported from prior author work appear in the load-bearing chain. The overall analysis is therefore a set of model-dependent explorations whose central claims retain independent content from the stated assumptions.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on models drawn from cosmological simulations of galaxy formation and on the introduction of clustering scenarios without first-principles derivation.

free parameters (1)
  • dark matter clustering model
    Suggested to enable significant capture contribution; no specific functional form or strength given in abstract.
axioms (2)
  • domain assumption Dense nuclear star cluster forms by cooling and collapse of gas while DM remains in a standard NFW profile
    Invoked to show that standard DM accretion is insignificant.
  • ad hoc to paper Dark matter clustering can occur possibly by self-interaction
    Introduced to make DM capture affect SMBH growth.

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