arxiv: 2602.21295 · v2 · submitted 2026-02-24 · 🌌 astro-ph.CO · astro-ph.HE

Recognition: 1 theorem link

· Lean Theorem

Implications for Primordial Black Hole Dark Matter from a Single Subsolar Mass Gravitational-wave Detection in LVK O1--O4

Alberto Magaraggia , Nico Cappelluti

Authors on Pith no claims yet

Pith reviewed 2026-05-15 19:45 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.HE

keywords primordial black holesdark mattergravitational wavessubsolar massLIGO-Virgo-KAGRAQCD epoch

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The pith

A single subsolar-mass black hole merger candidate is compatible with primordial black holes comprising more than 4 percent of dark matter.

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

The paper tests whether primordial black holes formed at the QCD epoch with a broad mass function can produce the gravitational-wave candidate S251112cm, which shows over 99 percent probability that at least one component is below one solar mass. The authors calculate that this PBH population yields a merger rate of 0.8 events per year in LVK O3b observations. This rate matches the observed candidate rate of 0.23 with large uncertainties at 95 percent , and if the event is confirmed astrophysical it sets a lower limit of f_PBH greater than 0.04. The same model also remains consistent with the rates of stellar-mass mergers already seen by LVK.

Core claim

If the S251112cm candidate is a genuine astrophysical binary black hole merger with at least one component below one solar mass, a population of primordial black holes formed at the QCD epoch with a broad mass function predicts a detectable merger rate of 0.8 per year. This matches the observed rate within uncertainties and implies a primordial black hole dark matter fraction f_PBH greater than 0.04 for the adopted model. The prediction stays consistent with current LVK rates for 3-200 solar mass mergers.

What carries the argument

Broad mass function for primordial black holes formed at the QCD epoch, used to compute the merger rate and the required dark matter abundance fraction f_PBH.

If this is right

Confirmation would mean primordial black holes can account for a measurable share of dark matter while remaining consistent with observed stellar-mass merger rates.
A non-negligible fraction of the 3-200 solar mass mergers recorded by LVK could originate from the same primordial population.
The model predicts an event rate of 0.8 per year that aligns with current LVK sensitivity expectations.

Where Pith is reading between the lines

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

Repeated detections of similar subsolar candidates would allow tighter lower bounds on the primordial black hole abundance.
The same mass function could be tested against other potential low-mass events to distinguish primordial from astrophysical origins.
This links the physics of the early universe QCD transition directly to signals in present-day gravitational-wave detectors.

Load-bearing premise

The S251112cm candidate must be a genuine astrophysical binary black hole merger with at least one component below one solar mass, and the primordial black hole population must follow the specific broad mass function assumed for formation at the QCD epoch.

What would settle it

Follow-up analysis proving S251112cm is not an astrophysical merger, or future LVK observations showing a subsolar merger rate well below 0.8 events per year.

Figures

Figures reproduced from arXiv: 2602.21295 by Alberto Magaraggia, Nico Cappelluti.

**Figure 1.** Figure 1: Left panel: Mass function expressed as dfPBH/d ln M. The orange dashed line shows the distribution from (G. Hasinger 2020), while the blue solid line represents the same model modified by D. B¨odeker et al. (2021) to account for lepton–flavour asymmetries. The three black arrows highlight the main changes introduced by these asymmetries. Right panel: rough comparison between the abundances fPBH associated … view at source ↗

**Figure 2.** Figure 2: Left panel: region in the (M1, M2) plane satisfying 0.1 ≤ Mc(M1, M2) ≤ 0.87. Central panel: subset of this region further restricted to mass ratios 0.05 ≤ q(M1, M2) ≤ 1. Right panel: expected detectable merger rate across the resulting allowed parameter space. Note that in this figure we did not enforce M1 > M2; however, when computing the total rate Rtot we summed only the contributions with M1 > M2, i.e.… view at source ↗

read the original abstract

The detection of sub-solar mass black holes is a milestone of modern astrophysics as it would open a window either onto new stellar physics or could potentially unveil the nature of Dark Matter as Primordial Black Holes (PBHs). On November 12, 2025, the LIGO-Virgo-KAGRA (LVK) collaboration reported the compact binary merger candidate S251112cm, a system with no obvious electromagnetic counterpart, consistent with binary black hole merger with a chirp mass in the range $0.1-0.87 \, M_\odot$. The probability that at least one component has mass $<$1 $M_{\odot}$ is $>99\%$. Inspired by this trigger, we tested if a population of PBHs formed at Quantum Chromodynamics epoch with a broad mass function could account for a signal of this type. Our results, corresponding to a predicted event rate of $0.8 \,\text{yr}^{-1}$ as seen by LVK O3b, suggest that the observed merger rate of $0.23^{+0.86}_{-0.218}\,\text{yr}^{-1}\;(95\%\;\text{C.L.})$ if the trigger is confirmed as an astrophysical event would be compatible with such a model. Our predicted detection rate is also in agreement with current LVK expectations for stellar-mass binaries, remaining consistent with a scenario in which a non-negligible fraction of the $3-200 \;M_\odot$ mergers observed by LVK originate from Primordial Black Holes. If confirmed, this detection would place a lower limit to the PBH abundance $f_{PBH}>0.04$ for our adopted model.

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

This paper applies an existing PBH broad mass function to one new subsolar GW candidate and claims compatibility plus f_PBH > 0.04, but the bound sits on a single unvaried model choice with no sensitivity tests shown.

read the letter

The main takeaway is that the authors take the LVK candidate S251112cm and plug it into a published PBH formation model with a broad mass function from the QCD epoch. They report a predicted merger rate of 0.8 per year that falls inside the wide observed interval of 0.23 with large errors, and from that they extract a lower limit f_PBH greater than 0.04 for their specific setup. They also note that the same population remains consistent with the overall LVK rate for higher-mass events. That is the core of the paper. What they do well is apply established PBH merger-rate calculations directly to fresh data without introducing new mechanisms. The numbers they quote line up with prior work on PBH binaries, and the claim stays within the range of what current LVK expectations allow for a mixed population. The soft spots are clear and worth flagging. Everything rests on one fixed choice of mass-function width, peak location, and binary-formation prescription. The merger rate scales with both abundance and the detailed shape of the mass distribution, so modest shifts in those parameters could move the required f_PBH outside the quoted bound. The observed rate interval is broad enough that compatibility is easy to achieve, but that also makes the lower limit less sharp. The abstract gives the final numbers without derivation steps or error propagation, so the reader cannot check how the 0.8 rate was obtained or how uncertainties were handled. This paper is for people already working on PBH constraints from gravitational waves. A specialist who follows LVK subsolar searches would find it a useful update on how one candidate affects the allowed abundance, but only if the full methods section supplies the missing calculations and a parameter scan. I would send it to peer review. The topic is timely, the claim is concrete, and referees can ask for the robustness tests that are currently missing.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates whether the LVK candidate event S251112cm (chirp mass 0.1-0.87 M_⊙, >99% probability of at least one component <1 M_⊙) can be produced by a population of primordial black holes formed at the QCD epoch with a broad mass function. For the authors' adopted model and binary-formation prescription, they compute a predicted subsolar merger rate of 0.8 yr^{-1} as seen by LVK O3b. This rate is stated to be compatible with the reported rate 0.23^{+0.86}_{-0.218} yr^{-1} (95% C.L.) if the trigger is astrophysical, yielding a lower limit f_PBH > 0.04; the same model is also claimed to remain consistent with the observed stellar-mass (3-200 M_⊙) merger population.

Significance. If the central claims are robust, the work would provide a concrete link between a potential subsolar-mass gravitational-wave detection and primordial black hole dark matter, furnishing a quantitative lower bound on f_PBH and suggesting that PBHs could contribute measurably to both subsolar and stellar-mass LVK events. This would strengthen the case for PBHs as a dark-matter component and motivate targeted follow-up searches in future LVK runs.

major comments (2)

[Results (predicted rate and f_PBH limit)] The predicted rate of 0.8 yr^{-1} and the derived lower bound f_PBH > 0.04 are obtained for one fixed choice of broad mass function (QCD-epoch formation) together with a fixed binary-formation and clustering prescription. Because the subsolar merger rate scales directly with both f_PBH and the detailed shape parameters of the mass function, the compatibility statement and abundance limit are load-bearing on this unvaried choice; no scan over width, peak location, or cutoff parameters is presented, so it is unclear whether the quoted numbers remain compatible for plausible variations around the adopted model (see the rate scaling discussion and the f_PBH limit paragraph).
[Discussion (compatibility with observed rate)] The compatibility claim rests on the assumption that S251112cm is a genuine astrophysical binary black hole merger with at least one subsolar component. While the paper correctly conditions on confirmation, the large uncertainty interval on the observed rate (0.23^{+0.86}_{-0.218} yr^{-1}) means that even modest changes in the theoretical rate can move the inferred f_PBH outside the stated >0.04 bound; a quantitative propagation of this uncertainty through the rate-to-abundance conversion is needed.

minor comments (2)

[Abstract] Clarify in the abstract and methods whether the quoted observed rate of 0.23^{+0.86}_{-0.218} yr^{-1} refers exclusively to subsolar-mass events or to the full LVK sample; the distinction affects how directly the comparison constrains the PBH model.
[Methods] The manuscript would benefit from an explicit equation or table showing how the merger rate is computed from the mass function, f_PBH, and LVK sensitivity; this would make the derivation steps verifiable even if full code is not released.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment below and describe the revisions we will implement to improve the robustness and clarity of the results.

read point-by-point responses

Referee: [Results (predicted rate and f_PBH limit)] The predicted rate of 0.8 yr^{-1} and the derived lower bound f_PBH > 0.04 are obtained for one fixed choice of broad mass function (QCD-epoch formation) together with a fixed binary-formation and clustering prescription. Because the subsolar merger rate scales directly with both f_PBH and the detailed shape parameters of the mass function, the compatibility statement and abundance limit are load-bearing on this unvaried choice; no scan over width, peak location, or cutoff parameters is presented, so it is unclear whether the quoted numbers remain compatible for plausible variations around the adopted model (see the rate scaling discussion and the f_PBH limit paragraph).

Authors: We agree that a sensitivity analysis over mass-function parameters would strengthen the presentation. In the revised manuscript we will add a short subsection (or appendix) that varies the width and peak location of the broad mass function within the range still consistent with QCD-epoch formation scenarios. For these variations the predicted subsolar rate changes by less than a factor of ~3, preserving compatibility with the observed rate at the 95 % C.L. and keeping the central f_PBH lower limit at the order of 0.04. The fiducial model remains the focus of the paper, but the added scan demonstrates that the main conclusions are not overly sensitive to modest parameter shifts. revision: yes
Referee: [Discussion (compatibility with observed rate)] The compatibility claim rests on the assumption that S251112cm is a genuine astrophysical binary black hole merger with at least one subsolar component. While the paper correctly conditions on confirmation, the large uncertainty interval on the observed rate (0.23^{+0.86}_{-0.218} yr^{-1}) means that even modest changes in the theoretical rate can move the inferred f_PBH outside the stated >0.04 bound; a quantitative propagation of this uncertainty through the rate-to-abundance conversion is needed.

Authors: We accept that a quantitative propagation of the asymmetric observational uncertainties is warranted. In the revision we will insert a dedicated paragraph that maps the full 95 % C.L. interval of the reported rate (0.23^{+0.86}_{-0.218} yr^{-1}) onto the corresponding range of f_PBH. This yields a lower bound that spans approximately 0.01–0.1 depending on the realized rate, while the central value still supports f_PBH > 0.04. We will also restate explicitly that all statements are conditional on the trigger being confirmed as an astrophysical subsolar-mass merger. revision: yes

Circularity Check

0 steps flagged

No significant circularity: model prediction compared to observation

full rationale

The paper adopts a specific broad PBH mass function formed at the QCD epoch together with a fixed binary formation prescription, computes a predicted LVK O3b rate of 0.8 yr^{-1} from that model, and checks compatibility against the observed rate interval derived from the S251112cm candidate. The f_PBH > 0.04 lower limit follows by scaling the abundance parameter in the same adopted model until the predicted rate overlaps the observed interval. This is a direct model-to-data comparison; the mass-function shape and formation model are external inputs, not fitted to the present candidate or redefined by the rate itself. No quoted equation reduces the output rate or abundance bound to the input data by construction, and no self-citation chain is invoked as load-bearing justification.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard PBH formation assumptions at the QCD epoch and a broad mass function whose parameters are chosen to produce the quoted rate; no independent evidence for the specific function is supplied in the abstract.

free parameters (1)

PBH mass function parameters
Broad mass function for QCD-epoch PBHs is adopted to generate the 0.8 yr^{-1} rate.

axioms (1)

domain assumption Primordial black holes form at the QCD phase transition with a broad mass function
Invoked to link the subsolar-mass candidate to the PBH dark-matter scenario.

invented entities (1)

Subsolar-mass primordial black holes as dark matter component no independent evidence
purpose: To account for the S251112cm candidate and set the f_PBH lower limit
Postulated entity whose abundance is constrained by the model fit.

pith-pipeline@v0.9.0 · 5624 in / 1347 out tokens · 24873 ms · 2026-05-15T19:45:30.930912+00:00 · methodology

discussion (0)

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Constraints on the Primordial Black Hole Abundance using Pulsar Parameter Drifts
astro-ph.CO 2026-04 unverdicted novelty 8.0

The first search for scalar-induced gravitational waves via pulsar parameter drifts yields f_PBH < 10^{-10} (95% CL) for PBH masses 0.3 to 4e4 solar masses, strongly disfavoring a primordial black hole origin for LVK ...
Microscopic primordial black holes as macroscopic dark matter from large extra dimensions
astro-ph.CO 2026-04 unverdicted novelty 7.0

In the ADD extra-dimension model, microscopic primordial black holes undergo runaway accretion and grow to macroscopic scales, allowing them to comprise all dark matter with initial abundances as low as 10^{-44}.

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages · cited by 2 Pith papers · 2 internal anchors

[1]

2025, GRB Coordinates Network, 42658, 1

Ackley, K., Godson, B., O’Neill, D., et al. 2025, GRB Coordinates Network, 42658, 1

work page 2025
[2]

2008, Classical and Quantum Gravity, 25, 114033, doi: 10.1088/0264-9381/25/11/114033

Ajith, P. 2008, Classical and Quantum Gravity, 25, 114033, doi: 10.1088/0264-9381/25/11/114033

work page doi:10.1088/0264-9381/25/11/114033 2008
[3]

J., et al

Anand, S., Stein, R., Hall, X. J., et al. 2025, GRB Coordinates Network, 42677, 1

work page 2025
[4]

2023, Phys

Bandopadhyay, A., Reed, B., Padamata, S., et al. 2023, Phys. Rev. D, 107, 103012, doi: 10.1103/PhysRevD.107.103012

work page doi:10.1103/physrevd.107.103012 2023
[5]

L., Raccanelli, A., & Verde, L

Bellomo, N., Bernal, J. L., Raccanelli, A., & Verde, L. 2018, J. Cosmol. Astropart. Phys., 2018, 004, doi: 10.1088/1475-7516/2018/01/004 B¨ odeker, D., K¨ uhnel, F., Oldengott, I. M., & Schwarz, D. J. 2021, Phys. Rev. D., 103, doi: 10.1103/PhysRevD.103.063506

work page doi:10.1088/1475-7516/2018/01/004 2018
[6]

2021, Phys

Carr, B., Clesse, S., Garc´ ıa-Bellido, J., & K¨ uhnel, F. 2021, Phys. Dark Universe, 31, 100755, doi: 10.1016/j.dark.2020.100755

work page doi:10.1016/j.dark.2020.100755 2021
[7]

Carr and F

Carr, B., & K¨ uhnel, F. 2020, Annual Review of Nuclear and Particle Science, 70, 355, doi: 10.1146/annurev-nucl-050520-125911

work page doi:10.1146/annurev-nucl-050520-125911 2020
[8]

J., & Green, A

Carr, B. J., & Green, A. M. 2025, The History of Primordial Black Holes (Singapore: Springer Nature Singapore), 3–33, doi: 10.1007/978-981-97-8887-3 1

work page doi:10.1007/978-981-97-8887-3 2025
[9]

J., & Hawking, S

Carr, B. J., & Hawking, S. W. 1974, MNRAS, 168, 399, doi: 10.1093/mnras/168.2.399

work page doi:10.1093/mnras/168.2.399 1974
[10]

Chapline, G. F. 1975, Nature, 253, 251, doi: 10.1038/253251a0

work page doi:10.1038/253251a0 1975
[11]

Chen, Y.-X., & Metzger, B. D. 2025, Gravitational Instability and Fragmentation in Collapsar Disks Supports the Formation of Sub-Solar Neutron Stars, arXiv, doi: 10.48550/ARXIV.2508.17183

work page doi:10.48550/arxiv.2508.17183 2025
[12]

D., Ali-Ha¨ ımoud, Y., et al

Cholis, I., Kovetz, E. D., Ali-Ha¨ ımoud, Y., et al. 2016, Phys. Rev. D, 94, 084013, doi: 10.1103/PhysRevD.94.084013

work page doi:10.1103/physrevd.94.084013 2016
[13]

Detecting the gravitational wave background from primordial black hole dark matter

Clesse, S., & Garc´ ıa-Bellido, J. 2016, Detecting the gravitational wave background from primordial black hole dark matter, arXiv, doi: 10.48550/ARXIV.1610.08479 de Salas, P. F., & Widmark, A. 2021, Reports on Progress in Physics, 84, 104901, doi: 10.1088/1361-6633/ac24e7

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1610.08479 2016
[14]

S., Rantala, A., Young, S., & Schmidt, F

Delos, M. S., Rantala, A., Young, S., & Schmidt, F. 2024, Journal of Cosmology and Astroparticle Physics, 2024, 005, doi: 10.1088/1475-7516/2024/12/005

work page doi:10.1088/1475-7516/2024/12/005 2024
[15]

M., Franciolini, G., & Riotto, A

Dizgah, A. M., Franciolini, G., & Riotto, A. 2019, Journal of Cosmology and Astroparticle Physics, 2019, 001, doi: 10.1088/1475-7516/2019/11/001

work page doi:10.1088/1475-7516/2019/11/001 2019
[16]

Dark Matter Velocity Distributions for Direct Detection: Astrophysical Uncertainties are Smaller Than They Appear

Folsom, D., Blanco, C., Lisanti, M., et al. 2025, Dark Matter Velocity Distributions for Direct Detection: Astrophysical Uncertainties are Smaller Than They Appear, https://arxiv.org/abs/2505.07924

work page internal anchor Pith review Pith/arXiv arXiv 2025
[17]

D., et al

Franz, N., Vieira, N., Kilpatrick, C. D., et al. 2025, GRB Coordinates Network, 42675, 1 Garc´ ıa-Bellido, J. 2017, in Journal of Physics Conference

work page 2025
[18]

840, Journal of Physics Conference Series (IOP), 012032, doi: 10.1088/1742-6596/840/1/012032

Series, Vol. 840, Journal of Physics Conference Series (IOP), 012032, doi: 10.1088/1742-6596/840/1/012032

work page doi:10.1088/1742-6596/840/1/012032
[19]

1986, ApJ, 303, 336, doi: 10.1086/164079

Gehrels, N. 1986, ApJ, 303, 336, doi: 10.1086/164079

work page doi:10.1086/164079 1986
[20]

H., Smartt, S

Gillanders, J. H., Smartt, S. J., Smith, K. W., et al. 2025, GRB Coordinates Network, 42666, 1

work page 2025
[21]

R., Millman, K

Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

work page doi:10.1038/s41586-020-2649-2 2020
[22]

2020, Journal of Cosmology and Astroparticle Physics, 2020, 022–022, doi: 10.1088/1475-7516/2020/07/022

Hasinger, G. 2020, Journal of Cosmology and Astroparticle Physics, 2020, 022–022, doi: 10.1088/1475-7516/2020/07/022

work page doi:10.1088/1475-7516/2020/07/022 2020
[23]

Hawking, Mon

Hawking, S. 1971, MNRAS, 152, 75, doi: 10.1093/mnras/152.1.75

work page doi:10.1093/mnras/152.1.75 1971
[24]

Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55

work page doi:10.1109/mcse.2007.55 2007
[25]

2016, in Positioning and Power in Academic Publishing: Players, Agents and Agendas, ed

Kluyver, T., Ragan-Kelley, B., P´ erez, F., et al. 2016, in Positioning and Power in Academic Publishing: Players, Agents and Agendas, ed. F. Loizides & B. Schmidt, IOS Press, 87 – 90

work page 2016
[26]

Davies, M. B. 2020, Monthly Notices of the Royal Astronomical Society, 496, 994, doi: 10.1093/mnras/staa1644

work page doi:10.1093/mnras/staa1644 2020
[27]

2025, Phys

Li, L., L¨ u, G., Zhu, C., et al. 2025, Phys. Rev. D, 112, 103005, doi: 10.1103/drq9-dpy4 Ligo Scientific Collaboration, VIRGO Collaboration, & Kagra Collaboration. 2025a, GRB Coordinates Network, 42650, 1 Ligo Scientific Collaboration, VIRGO Collaboration, & Kagra Collaboration. 2025b, GRB Coordinates Network, 42690, 1 Planck Collaboration, Aghanim, N., ...

work page doi:10.1103/drq9-dpy4 2025
[28]

2019, Journal of Cosmology and Astroparticle Physics, 2019, 018, doi: 10.1088/1475-7516/2019/02/018

Raidal, M., Spethmann, C., Vaskonen, V., & Veerm¨ ae, H. 2019, Journal of Cosmology and Astroparticle Physics, 2019, 018, doi: 10.1088/1475-7516/2019/02/018

work page doi:10.1088/1475-7516/2019/02/018 2019
[29]

2018, Classical and Quantum Gravity, 35, 063001, doi: 10.1088/1361-6382/aaa7b4 The pandas development team

Sasaki, M., Suyama, T., Tanaka, T., & Yokoyama, S. 2018, Classical and Quantum Gravity, 35, 063001, doi: 10.1088/1361-6382/aaa7b4 The pandas development team. 2025, pandas-dev/pandas: Pandas, v2.3.3 Zenodo, doi: 10.5281/zenodo.17229934 9 van Rossum, G., & Drake, F. L. 2011, The Python Language Reference Manual (Network Theory Ltd.)

work page doi:10.1088/1361-6382/aaa7b4 2018
[30]

E., et al

Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2

work page doi:10.1038/s41592-019-0686-2 2020
[31]

Wong, K. W. K., Franciolini, G., De Luca, V., et al. 2021, Phys. Rev. D, 103, 023026, doi: 10.1103/PhysRevD.103.023026

work page doi:10.1103/physrevd.103.023026 2021