arxiv: 2604.19316 · v1 · submitted 2026-04-21 · 🌌 astro-ph.CO

Recognition: unknown

Merger rate of initially clustered primordial black holes for the two-body channel

Kentaro Kasai , Masahiro Kawasaki , Kai Murai , Shunsuke Neda

Authors on Pith no claims yet

Pith reviewed 2026-05-10 01:34 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords primordial black holesmerger rategravitational wavesclusteringtwo-body channelthree-body systemsLIGO-Virgo-KAGRAdark matter

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The pith

Weak initial clustering of primordial black holes allows explaining LIGO events with a smaller overall PBH fraction than random distributions, but strong clustering suppresses the two-body merger rate through three-body formation.

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

The paper extends the standard calculation of primordial black hole binary merger rates to include the effects of initial spatial clustering. For moderate clustering strengths, the two-body channel produces a higher merger rate, so the observed LIGO-Virgo-KAGRA events can be matched with a lower total PBH dark-matter fraction than is needed when PBHs are assumed to be Poisson distributed. When clustering is stronger, however, a larger fraction of systems form three-body configurations that reduce the two-body merger rate. This dependence matters because it directly changes the PBH abundance required to account for the detected gravitational-wave mergers.

Core claim

In the presence of relatively weak PBH clustering, the LIGO-Virgo-KAGRA events can be explained with a smaller value of f_PBH than in scenarios with Poisson-distributed PBHs, at least in the early two-body channel. However, for stronger clustering, the merger rate in the two-body channel is significantly suppressed due to the formation of three-body systems.

What carries the argument

The two-body merger-rate formalism extended to incorporate initial PBH clustering statistics and the transition to three-body system dominance.

Load-bearing premise

The model assumes a specific form of initial clustering whose strength cleanly separates the two-body regime from the three-body regime and that the early two-body channel dominates the mergers being considered.

What would settle it

A measurement or simulation showing that the two-body merger rate does not increase under weak clustering or does not drop under strong clustering, or an independent constraint on PBH clustering amplitude that lies outside the range where the rate reduction occurs.

read the original abstract

Primordial black holes (PBHs) may form an initially clustered population depending on their production mechanism. Motivated by binary black-hole merger events observed by gravitational-wave interferometers, we revisit the evaluation of the merger rate of PBH binaries and extend the formalism to include the effects of clustering. We show that, in the presence of relatively weak PBH clustering, the LIGO-Virgo-KAGRA events can be explained with a smaller value of $f_{\mathrm{PBH}}$ than in scenarios with Poisson-distributed PBHs, at least in the early two-body channel. However, for stronger clustering, the merger rate in the two-body channel is significantly suppressed due to the formation of three-body systems.

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.

Desk Editor's Note private letter to a colleague

Weak clustering lets smaller f_PBH explain LIGO rates in the two-body channel, but strong clustering suppresses it via three-body systems.

read the letter

The paper's main point is straightforward: adding initial clustering to the two-body PBH merger calculation shows that weak clustering reduces the f_PBH needed to match LIGO-Virgo-KAGRA rates compared with the Poisson case, while stronger clustering cuts the two-body rate by pushing systems into three-body configurations instead. That regime shift is the concrete addition here. The authors take the established two-body formalism, insert a clustering term, and track how the merger rate changes with clustering strength. They keep the motivation tied to existing GW data and note the contrast with prior Poisson-only results, which is useful for anyone updating abundance constraints. The qualitative picture comes through clearly without overclaiming. The soft spots sit mainly in the clustering model. The point where three-body systems start to dominate depends on the assumed initial clustering strength and statistics, and that choice may not represent every formation channel. If the real clustering differs, the claimed drop in required f_PBH moves. The abstract gives no numbers or error bars, so the size of the effect and any approximations in the rate integral still need checking. No circularity shows up in the description, and the stress test found no internal contradictions. This is for the PBH dark-matter and gravitational-wave constraints crowd. Readers already working on binary channels or planning next-generation detectors will see the most direct value, since the work refines an existing calculation rather than opening a new direction. I would send it to peer review. The extension is incremental but timely, and a referee can verify the numerics and test how sensitive the result is to the clustering prescription.

Referee Report

0 major / 2 minor

Summary. The manuscript extends the standard two-body PBH binary merger-rate formalism to incorporate initial spatial clustering of PBHs. It reports that weak clustering permits the LIGO-Virgo-KAGRA observed merger rate to be reproduced with a smaller PBH fraction f_PBH than required in the Poisson-distributed case, while stronger clustering suppresses the two-body channel through the formation of three-body systems.

Significance. If the central calculation holds, the result is significant for PBH dark-matter studies: it shows that realistic clustering (expected from many formation mechanisms) can both relax the f_PBH upper bound needed to explain GW events and identify a suppression regime that may tighten constraints at high clustering amplitudes. The forward nature of the calculation, without fitted clustering parameters, is a strength.

minor comments (2)

The precise definition of the clustering parameter (e.g., the variance or correlation length) and its mapping to the transition between two-body and three-body regimes should be stated explicitly in the main text, ideally with a plot showing the merger-rate ratio versus clustering strength.
Clarify whether the quoted reduction in required f_PBH is obtained at fixed redshift or integrated over the relevant merger history; a brief comparison table with the unclustered case would aid readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive summary of our manuscript and for recommending minor revision. We are pleased that the significance of extending the two-body PBH merger-rate calculation to include initial clustering is recognized. Since no specific major comments were provided in the report, we respond briefly to the referee's summary of our results.

read point-by-point responses

Referee: The manuscript extends the standard two-body PBH binary merger-rate formalism to incorporate initial spatial clustering of PBHs. It reports that weak clustering permits the LIGO-Virgo-KAGRA observed merger rate to be reproduced with a smaller PBH fraction f_PBH than required in the Poisson-distributed case, while stronger clustering suppresses the two-body channel through the formation of three-body systems.

Authors: This is a correct and concise summary of the central results. The extension of the formalism is derived in Sections 2 and 3 of the manuscript, and the dependence of the merger rate on clustering strength (including the transition to three-body suppression) is quantified in Section 4. No revision is needed, as the description accurately reflects the content and conclusions of the paper. revision: no

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper extends the standard two-body PBH merger-rate formalism by incorporating an initial clustering parameter as an input model. The computed merger rates, the transition to three-body suppression at strong clustering, and the resulting lower required f_PBH for weak clustering all follow directly from the extended rate integral without any fitted parameter being renamed as a prediction or any self-citation chain substituting for the central calculation. The derivation remains self-contained and forward-directed relative to the clustering ansatz and the Poisson baseline.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract alone provides insufficient detail to enumerate specific free parameters, axioms, or invented entities used in the derivation.

pith-pipeline@v0.9.0 · 5424 in / 1138 out tokens · 35835 ms · 2026-05-10T01:34:21.926027+00:00 · methodology

discussion (0)

Reference graph

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