arxiv: 2604.14247 · v1 · submitted 2026-04-15 · 🌌 astro-ph.GA · astro-ph.HE· gr-qc

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Could the high-mass black holes from gravitational-wave observations be explained by lensing?

Ritesh Harshe , R. Prasad , Parameswaran Ajith

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:07 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.HEgr-qc

keywords gravitational lensingbinary black holesLIGO-Virgo observationsgravitational wavesmass distributionredshift distributionstochastic background

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The pith

Lensing magnification cannot explain the high-mass black holes seen by LIGO and Virgo.

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

The paper tests whether gravitational lensing can account for the unexpectedly high masses of black holes in binary mergers detected by LIGO and Virgo. It does so by running simulations of lensed events under the BDS model, which assumes an underlying mass distribution like that of galactic black holes plus a specific redshift distribution for mergers, then checks consistency against four independent sets of observations. The comparisons cover the total number of detected mergers, the joint distribution of redshifted total mass and apparent luminosity distance, the absence of strongly lensed events, and the non-detection of a stochastic gravitational-wave background. No choice of model parameters satisfies all constraints at once. The authors therefore conclude that lensing is not responsible for the apparent high masses.

Core claim

Simulations of lensed BBH mergers with the BDS model show that it is inconsistent with the observed number of BBH mergers, the joint distribution of redshifted total mass and apparent luminosity distance, the non-detection of strongly lensed events, and the non-observation of the stochastic GW background. Therefore, gravitational lensing is not a viable explanation for the high-mass black holes discovered by LIGO and Virgo.

What carries the argument

Numerical simulations of lensed binary black hole mergers that incorporate the BDS redshift distribution and lensing magnification, then tested for consistency against multiple LIGO-Virgo observational constraints.

If this is right

High-mass black holes in mergers must originate from intrinsic processes such as the collapse of metal-poor massive stars.
Population models for future gravitational-wave forecasts should treat the observed masses as close to the true masses without lensing corrections.
The non-detection of a stochastic background already limits the allowed merger rate density under lensing scenarios.
Searches for strongly lensed events can proceed without expecting a large hidden population from the BDS redshift distribution.

Where Pith is reading between the lines

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

The result tightens the requirement that alternative channels, such as hierarchical mergers in dense clusters, must produce the observed high-mass population.
Similar lensing-based reinterpretations of other gravitational-wave anomalies should be subjected to the same multi-observable consistency tests.
Refined forecasts for third-generation detectors can now exclude lensing as a dominant bias when estimating intrinsic black-hole mass functions.

Load-bearing premise

The simulations accurately capture the joint effects of lensing magnification, selection biases in LIGO-Virgo detection, and the proposed redshift distribution without unaccounted systematic errors in apparent luminosity distance or event rates.

What would settle it

Detection of even one strongly lensed BBH event showing multiple images, or a future measurement of the stochastic gravitational-wave background amplitude that matches the BDS-predicted rates, would indicate that the model can be made consistent with observations.

Figures

Figures reproduced from arXiv: 2604.14247 by Parameswaran Ajith, Ritesh Harshe, R. Prasad.

**Figure 1.** Figure 1: Dotted-dashed lines show the BDS merger rate R(z) for different values of the model parameters A1 in units of yr−1 Gpc−3 and th in units of Gyr (shown in legends). In contrast, the shaded band shows the merger rates predicted by various population synthesis models in the literature. The black curve corresponds to the same obtained from the star formation model of Madau & Dickinson (2014) that is scaled w… view at source ↗

**Figure 2.** Figure 2: The expected number of detectable GW events Λ as a function of BDS model parameters A1 and th. We draw contours of Λ = 60 and 115 (number of GW detections in O1-O2-O3, including Poisson uncertainties; see text and Appendix A for more details). A large region of parameter space is inconsistent with this constraint. 0.5 1.0 1.5 2.0 th [Gyr] 103 104 105 A1 [yr −1Gpc − 3 ] 6.3 1 2 3 5 10 15 20 25 30 u × 100 [… view at source ↗

**Figure 3.** Figure 3: The expected percent of detectable strongly lensed pairs as a function of A1 and th. The 3σ upper bound on the observed strong lensing fraction is ∼ 6.3% (see Appendix D). The region with a larger fraction than this bound is inconsistent with the data. (see Appendix D). The region of the parameter space where the predicted fraction exceeds the upper bound is inconsistent with the observations. This elimin… view at source ↗

**Figure 4.** Figure 4: The posterior distribution of A1, th estimated from the consistency of the predicted distribution of the redshifted total mass and apparent luminosity distance with the corresponding posteriors of the observed events. The 3σ lower/upper bounds are marked by vertical dashed lines. 0.5 1.0 1.5 2.0 th [Gyr] 103 104 105 A1 [yr −1Gpc − 3 ] 3 2 0 2 4 6 8 10 12 14 SNR [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: The SGWB SNR as a function of A1 and th. We draw contours of SNR of 2 and 3 (which correspond to a 2σ and 3σ detection of SGWB, respectively). The parameter space above an SNR of 3 can be rejected because of the non-detection of SGWB in current observations. (2019); Mandel et al. (2019). We then compute the 3σ credible region of the posterior, which is shown in figure 4. The posterior peaks at th ≃ 0.95 G… view at source ↗

**Figure 7.** Figure 7: The posterior on the Poisson mean of the distribution of the number of detectable events. The bounds Λ ∼ 60 and Λ ∼ 115 enclose the 3σ bounds on the Poisson mean Λ. A. CONSTRAINTS ON DETECTABLE EVENTS We assume that the number Ndet of detected GW events follows a Poisson distribution with mean Λ. Given Λ, the likelihood of detecting Ndet events is P(Ndet|Λ) = Λ Ndet exp(−Λ)/Ndet!. From O1-O2-O3 data, Ndet … view at source ↗

**Figure 9.** Figure 9: shows the posterior and 3σ upper bound on the observed strong lensing fraction u given the set of B ovlp values from O1-O1, O2-O2, O3a-O3a, and O3b-O3b pairs. The lensing fraction is consistent with being zero, with a 3σ upper limit of 6.3% [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗

**Figure 10.** Figure 10: shows the predicted lensing fraction by the BDS model as a function of the parameter th, as well as its 3σ 0.00 0.05 0.10 0.15 0.20 0.25 u 10−10 10−7 10−4 10−1 P ( u|Bovlp ) u = 0.063 [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗

**Figure 11.** Figure 11: The blue contours show the distribution of the redshifted total mass and apparent luminosity distance of all the detected events inferred from the data. The orange and green contours correspond to the prediction of the BDS model with parameters th = 1.0 Gyr (close to the best fit value in our analysis) and th = 1.25 Gyr (the optimal choice as claimed by BDS). None of the model choices are particularly… view at source ↗

read the original abstract

The high-mass ($M \gtrsim 30 M_\odot$) black holes (BHs) from the gravitational-wave (GW) observations of LIGO and Virgo came as a surprise to many astronomers. While the collapse of metal-poor massive stars could produce such BHs, gravitational lensing has been invoked to explain their high masses. Broadhurst, Diego, and Smoot (henceforth BDS) argued that the mass distribution of BHs in coalescing binaries is very similar to that of the galactic BHs, and the inferred high masses are the result of neglecting the lensing magnification. They also proposed a redshift distribution of binary BH (BBH) mergers to explain the observed LIGO-Virgo mass distribution. We ask whether such a model is consistent with different aspects of the GW observations: 1) the observed number of BBH mergers, 2) the distribution of their redshifted total mass and apparent luminosity distance, 3) the non-detection of strongly lensed events, and 4) the non-observation of the stochastic GW background. By simulating lensed BBH mergers with the BDS model and comparing them with observations, we conclude that no choice of BDS model parameters is consistent with all aspects of the observations. Lensing magnification is not a viable explanation for the high-mass BHs discovered by LIGO and Virgo.

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

Simulations show the BDS lensing model fails to match all GW observations at once, ruling it out as an explanation for high-mass black holes.

read the letter

The main point here is that lensing magnification, as proposed in the BDS model, does not explain the high-mass black holes from gravitational-wave observations. The simulations show inconsistencies across several key observables no matter how the parameters are adjusted. The new element is running forward simulations of lensed binary black hole mergers that incorporate the BDS redshift distribution and then comparing the results directly to four independent pieces of data: the observed merger rate, the distribution of redshifted masses and apparent distances, the lack of strongly lensed events, and the non-detection of a stochastic background. This goes beyond the original suggestion by putting the full model to a joint test. The paper does a solid job of laying out these checks in a clear way and arriving at a negative result without overclaiming. The approach avoids circularity by using external model inputs and public summaries rather than fitting to the target data. The main limitation is that the abstract leaves the precise treatment of selection effects and error modeling to the methods section, which we don't have here. That said, the multi-constraint strategy makes it less likely that overlooked systematics could fix everything at once. The stress-test note also finds no obvious internal problems. This work is aimed at the community studying black hole formation and binary evolution in the context of gravitational waves. A reader interested in alternative explanations for the mass spectrum would get value from seeing this specific model ruled out. It is worth a serious referee because it provides concrete, falsifiable tests rather than just discussion. I recommend putting it through peer review.

Referee Report

0 major / 2 minor

Summary. The manuscript simulates lensed binary black hole (BBH) merger populations under the Broadhurst-Diego-Smoot (BDS) model and tests consistency against four independent LIGO-Virgo constraints: the observed BBH event rate, the joint distribution of redshifted total mass and apparent luminosity distance, the non-detection of strongly lensed events, and the non-observation of the stochastic gravitational-wave background. Forward modeling shows that no choice of BDS parameters simultaneously satisfies all four observables, leading to the conclusion that lensing magnification cannot explain the high-mass black holes in the GW catalog.

Significance. If the simulations correctly incorporate selection effects and magnification statistics, the multi-constraint rejection of the BDS scenario provides strong evidence against lensing as the origin of the apparent high-mass BH population. This supports astrophysical interpretations (e.g., formation in metal-poor environments) and demonstrates the value of exhaustive forward modeling against public summary statistics rather than fitting to the target data. The absence of free parameters tuned to the LIGO-Virgo sample is a methodological strength.

minor comments (2)

[Methods] The handling of LIGO-Virgo detection efficiency, luminosity-distance errors, and the precise form of the magnification PDF should be expanded in the methods section with explicit equations or pseudocode to enable independent reproduction of the four constraint comparisons.
[Results] Figure captions for the mass-distance and rate plots should explicitly state the assumed cosmology, the redshift range of the simulated population, and the exact observational data sets (e.g., GWTC-3 or specific catalog releases) used for comparison.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending minor revision. The referee's summary accurately reflects our main result: that no choice of parameters in the BDS lensing model is simultaneously consistent with the observed BBH rate, the joint mass-distance distribution, the absence of strongly lensed events, and the non-detection of the stochastic background. We appreciate the recognition of our forward-modeling approach and the absence of tuning to the LIGO-Virgo catalog. As no specific major comments were raised in the report, we have no point-by-point rebuttals to provide. We will incorporate any minor editorial suggestions in the revised version.

Circularity Check

0 steps flagged

No significant circularity in forward simulation and comparison

full rationale

The paper takes the external BDS model (Broadhurst et al.), performs forward simulations of lensed BBH populations, and compares the resulting predictions for event rates, mass-distance joint distributions, absence of strongly lensed events, and stochastic background against independent public observational summaries. No parameters are fitted to the target LIGO-Virgo data inside the derivation, and no self-citations or ansatzes are used to justify load-bearing steps. The multi-constraint rejection is therefore a genuine test rather than a re-expression of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard cosmological lensing and gravitational-wave detection models without introducing new entities or ad-hoc parameters beyond those already present in the BDS proposal being tested.

axioms (1)

domain assumption Standard assumptions about binary black hole population distributions, gravitational lensing magnification statistics, and LIGO-Virgo selection functions hold in the simulated catalogs.
Invoked when generating the mock lensed events and comparing their apparent properties to real detections.

pith-pipeline@v0.9.0 · 5558 in / 1277 out tokens · 59092 ms · 2026-05-10T13:07:45.155887+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.

How do the LIGO-Virgo-KAGRA's Heavy Black Holes Form? No evidence for core-collapse Intermediate-mass black holes in GWTC-4
astro-ph.HE 2026-05 unverdicted novelty 5.0

No evidence for core-collapse IMBHs in GWTC-4; heavy BHs from hierarchical mergers, with low-spin mass distribution truncating at ~65 solar masses and PIMG upper edge estimated at 150 solar masses.
How do the LIGO-Virgo-KAGRA's Heavy Black Holes Form? No evidence for core-collapse Intermediate-mass black holes in GWTC-4
astro-ph.HE 2026-05 unverdicted novelty 5.0

No evidence for core-collapse formed low-spin IMBHs in GWTC-4, with 90% upper limit on merger rate of 0.077 Gpc^{-3} yr^{-1}, low-spin BH mass truncation at 65 solar masses consistent with pair-instability gap lower e...

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3 extracted references · 1 canonical work pages · cited by 1 Pith paper

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work page doi:10.5281/zenodo.831784 2021