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arxiv: 2605.12858 · v1 · pith:2EAMNRZGnew · submitted 2026-05-13 · 🌌 astro-ph.HE · astro-ph.GA· astro-ph.SR

Forbidden Formation Histories: The Binary Black Hole Merger Rate Disfavors Long Delay Times

Aryanna Schiebelbein-Zwack , Maya Fishbach This is my paper

Pith reviewed 2026-06-30 22:01 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.GAastro-ph.SR
keywords binary black holesdelay time distributionmerger rate evolutiongravitational wavesprogenitor formation ratepopulation synthesisGWTC-4.0redshift evolution
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The pith

The observed binary black hole merger rate evolution forbids delay time distributions with long tails.

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

The redshift evolution of the binary black hole merger rate arises as the convolution of the progenitor formation rate with the distribution of time delays between formation and merger. Starting from data-driven fits to the merger rate versus redshift, deconvolution shows that some delay time distributions are physically incompatible because their long-delay tails force the inferred progenitor formation rate to become negative or unphysical at low redshifts. These forbidden distributions overpredict low-redshift mergers no matter what formation history is assumed. The analysis finds that the GWTC-4.0 data require a steeper decline in progenitor formation toward low redshift than the global star formation rate and are in tension with shallow power-law delay distributions such as those predicted for stable mass transfer. Imposing population synthesis delay times as a prior also shifts the inferred merger rate to a shallower evolution at intermediate redshifts.

Core claim

For a given evolution of the binary black hole merger rate, certain delay time distributions are forbidden because their long-delay tails overpredict low redshift mergers independently of any assumption about the progenitor formation rate. Using delay-time distributions derived from the COMPAS population synthesis code in combination with the BBH merger rate inferred from GWTC-4.0, the permitted progenitor formation histories decline more steeply toward low redshift than the global star formation rate, and the data are in tension with formation channels that predict shallow power-law delay-time distributions with indices α ≳ -0.7.

What carries the argument

Deconvolution of the observed merger rate evolution into a delay time distribution and progenitor formation rate, identifying delay time distributions whose long tails force unphysical (negative) formation rates at low redshift.

If this is right

  • Permitted progenitor formation histories decline more steeply at low redshift than the global star formation rate.
  • Delay time distributions with power-law indices α ≳ -0.7 are incompatible with the observed merger rate evolution.
  • Imposing COMPAS delay time distributions as a prior reduces the median inferred merger rate by 10 percent at redshift 1.5.
  • The method directly evaluates compatibility of specific population synthesis parameters with gravitational wave data.

Where Pith is reading between the lines

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

  • The same deconvolution approach could be applied to neutron star merger rates to test whether similar delay time restrictions appear.
  • Improved merger rate measurements at redshifts above 2 could further narrow the range of allowed delay time distributions.
  • Tension with stable mass transfer channels implies that other binary evolution pathways must dominate the observed population.

Load-bearing premise

The shape of the binary black hole merger rate versus redshift from GWTC-4.0 is taken as a fixed input whose uncertainties do not affect the identification of forbidden delay time distributions.

What would settle it

A measurement of the binary black hole merger rate at redshift 0.5 that lies substantially above the GWTC-4.0 inference, which would allow long-delay tails without requiring negative formation rates.

Figures

Figures reproduced from arXiv: 2605.12858 by Aryanna Schiebelbein-Zwack, Maya Fishbach.

Figure 1
Figure 1. Figure 1: Random draws of the computed BBH progenitor formation rate as a function of cosmic time (or equivalently, redshift), Rform(t), obtained by deconvolving the GWTC￾4.0 BBH merger rate posterior draws, Rmerge(t), and delay time distributions, p(τ ), from COMPAS. The formation rates that remain positive, and are therefore physical, throughout the observable redshift range are shown in purple, and those that dro… view at source ↗
Figure 2
Figure 2. Figure 2: An example GWTC-4.0 merger rate posterior curve (black) compared with the reconstructed formation rate (blue dotted) for p(τ ) ∝ τ −1 (left) and p(τ ) ∝ τ −1.5 (right). The dashed pink line shows the merger rate obtained by reconvolving the physically allowed (non-negative) formation rate with the specified time delay distribution. In other words, this is the merger rate implied by the cumulative contribut… view at source ↗
Figure 4
Figure 4. Figure 4: The distribution of delay times from COMPAS simulations (solid) and analytic power laws (dotted). The colour of each curve represents the fraction of the GWTC￾4.0 merger rate posterior that is consistent with a physical formation history under the given delay time distribution. The steeper the delay time distribution, and the higher the probability density at short delay times, the higher the com￾patibilit… view at source ↗
Figure 5
Figure 5. Figure 5: The compatibility of various assumptions for the COMPAS mass transfer efficiency parameter β with the GWTC-4.0 data. As β, the fraction of mass successfully ac￾creted during mass transfer, increases, the compatibility de￾creases. In other words, GWTC-4.0 disfavours large values of β. This is because larger β corresponds to higher reten￾tion of angular momentum, a higher orbital separation, and longer time … view at source ↗
Figure 7
Figure 7. Figure 7: The critical time delay distribution index α as a function of merger rate evolution index κ. For a specific κ, the delay time index α is constrained to be below the black boundary curve. The region above the curve is physically forbidden, as all α–κ combinations here result in negative progenitor formation rates. The blue shaded band illustrates the GWTC-4.0 90% credible interval for κ, as well as the me￾d… view at source ↗
read the original abstract

The redshift evolution of the binary black hole (BBH) merger rate can be expressed as the convolution of the progenitor formation rate with the distribution of time delays between formation and merger. We show that starting with data-driven fits to the BBH merger rate as a function of redshift, deconvolving the inferred BBH merger rate into a delay time distribution and progenitor formation rate exposes physically incompatible delay time distributions. For a given evolution of the merger rate, certain delay time distributions are forbidden because their long-delay tails overpredict low redshift mergers independently of any assumption about the progenitor formation rate. Using delay-time distributions derived from the COMPAS population synthesis code in combination with the BBH merger rate inferred from GWTC-4.0, we reconstruct the physically permitted progenitor formation histories and find a steeper decline toward low redshift than the global star formation rate. We also find that the GWTC-4.0 data are in tension with formation channels that predict shallow power-law delay-time distributions ($\alpha \gtrsim -0.7$), such as stable mass transfer. Conversely, imposing the COMPAS predictions for the delay time distribution as a prior reduces the median merger rate inferred in GWTC-4.0 by 10% at $z=1.5$, favoring a shallower merger rate evolution than the standard GWTC-4.0 inference. Additionally, we demonstrate that our method can constrain binary evolution physics by directly evaluating the compatibility of population synthesis parameters with gravitational wave observations. Our framework provides a model-independent avenue for ruling out regions of binary evolution and merger rate parameter space.

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

1 major / 1 minor

Summary. The paper claims that deconvolving data-driven fits to the BBH merger rate R(z) from GWTC-4.0 into a delay-time distribution (DTD) and progenitor formation rate reveals certain DTDs to be 'forbidden' because their long-delay tails overpredict low-redshift mergers for any non-negative formation-rate history. Using COMPAS-derived DTDs, the permitted formation histories decline more steeply at low redshift than the global star-formation rate; the GWTC-4.0 data are in tension with shallow power-law DTDs (α ≳ -0.7); imposing COMPAS DTDs as a prior lowers the median inferred merger rate by 10% at z=1.5; and the framework can directly constrain binary-evolution parameters.

Significance. If the central claim survives the noted robustness checks, the approach supplies a model-independent route to exclude regions of binary-evolution parameter space (e.g., stable mass-transfer channels) directly from the shape of R(z), independent of any specific star-formation-rate assumption. The quantitative 10% shift in the inferred merger rate when a COMPAS DTD prior is imposed illustrates the method's practical effect on existing GWTC inferences.

major comments (1)
  1. [Abstract] Abstract and the deconvolution procedure: the claim that certain DTDs are 'forbidden' is established by deconvolving a single (median) data-driven fit to R(z) from GWTC-4.0. The GWTC-4.0 posterior on R(z) has substantial width at z ≳ 1; a DTD ruled out by the median may still admit a non-negative formation-rate solution for other posterior draws. The manuscript does not demonstrate that the forbidden region is stable across the full posterior, which is load-bearing for the central claim that these DTDs are physically incompatible independent of progenitor assumptions.
minor comments (1)
  1. The manuscript does not indicate whether code or posterior samples used for the deconvolution are made available; releasing them would facilitate independent verification of the compatibility checks.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and insightful comments. We address the major comment below and will revise the manuscript to strengthen the robustness of the central claim.

read point-by-point responses

  1. Referee: [Abstract] Abstract and the deconvolution procedure: the claim that certain DTDs are 'forbidden' is established by deconvolving a single (median) data-driven fit to R(z) from GWTC-4.0. The GWTC-4.0 posterior on R(z) has substantial width at z ≳ 1; a DTD ruled out by the median may still admit a non-negative formation-rate solution for other posterior draws. The manuscript does not demonstrate that the forbidden region is stable across the full posterior, which is load-bearing for the central claim that these DTDs are physically incompatible independent of progenitor assumptions.

    Authors: We agree that the current analysis relies on the median R(z) fit and that demonstrating stability across the full GWTC-4.0 posterior is important for the claim. In the revised manuscript we will sample multiple posterior draws of R(z), repeat the deconvolution for each, and show that the excluded DTD regions (including shallow power laws with α ≳ -0.7) remain forbidden for the large majority of draws. This will confirm that the incompatibility is robust rather than an artifact of the median. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses external GWTC-4.0 input via direct deconvolution

full rationale

The paper's central claim follows from taking the GWTC-4.0 data-driven R(z) fit as an external input, then applying mathematical deconvolution with an assumed DTD to solve for the required progenitor formation rate. A DTD is declared forbidden only when no non-negative formation-rate solution exists for that fixed R(z). This is a direct computation from the input, not a self-definitional loop, fitted parameter renamed as prediction, or self-citation chain. The text contains no load-bearing self-citations or ansatzes smuggled via prior work. The result is conditional on the external benchmark and does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the accuracy of the GWTC-4.0 merger rate fit and on the validity of the deconvolution step; no new physical entities are introduced.

axioms (1)
  • domain assumption The observed BBH merger rate versus redshift can be expressed as the convolution of progenitor formation rate and delay time distribution.
    Stated in the first sentence of the abstract; this is the starting point for the deconvolution.

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Forward citations

Cited by 1 Pith paper

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

  1. Joint population and strong-lensing inference for resolved gravitational-wave events probes the black-hole merger rate beyond the peak of star formation

    astro-ph.HE 2026-06 unverdicted novelty 6.0

    Joint strong-lensing and population inference on resolved gravitational-wave events finds no lensed events and tightens constraints on the black-hole merger rate peak redshift and high-redshift tail.

Reference graph

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