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arxiv: 2606.05322 · v1 · pith:W3GHIMQ3new · submitted 2026-06-03 · 🌌 astro-ph.HE · astro-ph.SR

How Common Are Common Envelopes? Quantifying Their Role in Forming Gravitational-Wave Sources

Floor S. Broekgaarden , Ana Lam , Sasha Levina , Jakub Klencki , Kyle A. Rocha , Lieke van Son , Steffani M. Grondin , Monica Gallegos-Garcia
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Brian D. Metzger Enrico Ramirez-Ruiz Angela Twum Melanie Santiago Julia Haynes Tyler B. Smith Amedeo Romagnolo Edo Berger Lucas M. de S\'a
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Pith reviewed 2026-06-28 04:42 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.SR
keywords common envelope evolutiongravitational wave sourcesbinary population synthesisbinary black holesbinary neutron starsformation channelsmerger rates
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The pith

Binary black hole and black hole-neutron star mergers can form with or without common-envelope evolution while producing similar rates.

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

The paper compiles predictions from more than 200 isolated binary population synthesis simulations to quantify the role of common-envelope evolution in forming gravitational-wave sources. It finds that black hole binary and black hole-neutron star formation pathways range from zero to one hundred percent common-envelope involvement, yet different pathways often predict similar merger rates. This reveals a degeneracy in which merger rate measurements cannot uniquely determine the evolutionary pathways. Binary neutron star formation, however, almost always involves at least one common-envelope phase. The differences arise from assumptions on mass transfer stability, angular momentum loss, common-envelope efficiency, and supernova physics that interact in complex ways.

Core claim

By organizing more than 200 population-synthesis simulations in a unified hierarchical taxonomy of formation channels, the analysis shows that BBH and BHNS formation spans the full allowed range of common-envelope involvement from 0 to 100 percent while often yielding comparable merger rates, which establishes a fundamental degeneracy that prevents merger-rate measurements from uniquely constraining the underlying evolutionary pathways. In contrast, BNS formation proceeds almost exclusively through channels involving at least one common-envelope phase with fractions above 90 to 100 percent.

What carries the argument

A unified hierarchical taxonomy that classifies formation channels according to whether they involve common-envelope evolution or not, allowing systematic comparison across different simulation codes.

Load-bearing premise

The compiled set of more than 200 simulations provides an unbiased and sufficiently complete sampling of the range of possible formation-channel predictions under current modeling frameworks.

What would settle it

An observational measurement showing that fewer than 90 percent of binary neutron star mergers involve a common-envelope phase would contradict the central finding for BNS systems.

Figures

Figures reproduced from arXiv: 2606.05322 by Amedeo Romagnolo, Ana Lam, Angela Twum, Brian D. Metzger, Edo Berger, Enrico Ramirez-Ruiz, Floor S. Broekgaarden, Jakub Klencki, Julia Haynes, Kyle A. Rocha, Lieke van Son, Lucas M. de S\'a, Melanie Santiago, Monica Gallegos-Garcia, Sasha Levina, Steffani M. Grondin, Tyler B. Smith.

Figure 1
Figure 1. Figure 1: — Hierarchical formation-channel taxonomy used in this work to compile intrinsic merger rates from isolated binary evolution simulations of BBH, BHNS, and BNS systems. Level 1 partitions mergers into systems evolving without CE (no CE episodes), with CE (one or more CE episodes), and an other category for residual contributions where the original study does not further specify the CE involvement. Throughou… view at source ↗
Figure 2
Figure 2. Figure 2: — Global overview of Level 1 formation-channel diversity across the compiled population-synthesis simulations. Each point shows the fraction of systems forming without a CE phase for a given model, for BBH, BHNS, and BNS mergers. Data points are given a small random vertical offset for visualization clarity. BBH and BHNS populations span nearly the full range from CE-dominated to without-CE–dominated forma… view at source ↗
Figure 3
Figure 3. Figure 3: — Middle panel: Fractional contributions of Level 1 formation pathways (with and without CE) to the astrophysical BBH population across the compiled simulations. See [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: — Same as [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: — Same as [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: — Detailed Level 2 decomposition of BBH formation channels across the compiled population-synthesis simulations. Each horizontal bar represents a simulation, showing the fractional contribution of individual evolutionary subchannels within the isolated binary evolution paradigm. Subchannels are grouped into systems that evolve without a common-envelope (CE) phase (e.g., sequences involving only stable mass… view at source ↗
Figure 7
Figure 7. Figure 7: — Same as [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: — Same as [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: — Top: Fraction of BBH mergers forming without a CE phase as a function of the total BBH intrinsic merger rate for the compiled population-synthesis simulations. Each point represents a single model, colored by study or stellar-evolution code. Lines connect models within the same study that vary a single parameter, illustrating the impact of controlled parameter changes. Bottom: Same data grouped by study … view at source ↗
Figure 11
Figure 11. Figure 11: — Change in the fraction of systems forming without a CE phase as a function of parameter-family variations for BBH (top) and BHNS (bottom) populations. Each scatter point shows the relative change in the without-CE fraction within a given study when varying a single model parameter, grouped by parameter family. Scatter points correspond to individual simulation varia￾tions within each family, while horiz… view at source ↗
Figure 10
Figure 10. Figure 10: — Same as [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 13
Figure 13. Figure 13: — Same as [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: — Dependence of the fraction of BBH mergers forming without a CE phase on commonly varied binary-evolution parameters. Each panel shows simulations in which a single parameter is varied while other assumptions are kept fixed within the same population-synthesis study. Shown parameters in￾clude the angular momentum loss parameter 𝛾, CE efficiency parameter 𝛼CE, the mass-transfer efficiency 𝛽, supernova nat… view at source ↗
Figure 14
Figure 14. Figure 14: — Formation-channel fractions as a function of metallicity for compact-object binaries across multiple population-synthesis studies and literature constraints. Models are shown from Iorio et al. (2023b), Broekgaarden et al. (2022c), Van Son et al. (2024), and Neijssel et al. (2019) (a single BBH model), while colored markers indicate literature constraints at specific metallicities compiled in [PITH_FULL… view at source ↗
Figure 15
Figure 15. Figure 15: — [PITH_FULL_IMAGE:figures/full_fig_p042_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: — Without-CE versus with-CE intrinsic BBH merger rates for the compiled BBH population-synthesis simulations. Scatter symbols, colors, and connecting lines are as in the bottom panel of [PITH_FULL_IMAGE:figures/full_fig_p043_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: — Same as 16 for BHNS mergers. See GitHub for details and code [PITH_FULL_IMAGE:figures/full_fig_p044_17.png] view at source ↗
read the original abstract

A central goal of gravitational-wave astronomy is to use merging binary black hole (BBH), black hole-neutron star (BHNS), and binary neutron star (BNS) systems as fossils to reconstruct the formation and evolution of massive stars across cosmic time. In practice, this inference relies on population-synthesis models that map massive stellar binaries to merging compact objects. However, these models disagree on the dominant orbital-hardening mechanisms within isolated binary evolution, particularly on whether common-envelope (CE) evolution is required. To address this, we compile and systematically compare formation-channel predictions from more than 200 isolated-binary population-synthesis simulations, organized within a unified hierarchical taxonomy. We find that BBH and BHNS formation pathways span nearly the full allowed range from CE-dominated to without-CE-dominated evolution (0-100%), while often predicting similar merger rates, revealing a fundamental degeneracy: merger-rate measurements alone do not uniquely constrain the underlying evolutionary pathways. In contrast, BNS formation proceeds almost exclusively through channels involving at least one CE phase (>90-100%), suggesting CE evolution plays a qualitatively different role in BNS than in BBH and BHNS formation. The relative contributions of with-CE and without-CE pathways are governed primarily by assumptions controlling mass-transfer stability, angular-momentum loss, CE efficiency, and supernova physics, which often act non-linearly and in correlated fashion, such that trends from one-at-a-time parameter variations do not generalize across simulation frameworks. Robust interpretation of gravitational-wave populations will therefore require transparent formation-channel definitions, reproducible analysis pipelines, systematic cross-code comparisons, and observational constraints that extend beyond merger rates alone.

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 / 2 minor

Summary. The manuscript compiles and compares formation-channel predictions from more than 200 isolated-binary population-synthesis simulations, organized in a unified hierarchical taxonomy. It reports that BBH and BHNS pathways span nearly the full 0–100% range of CE versus without-CE contributions while often yielding similar merger rates, implying a degeneracy in which merger-rate measurements alone cannot uniquely constrain evolutionary pathways; by contrast, BNS formation is almost exclusively (>90–100%) CE-involved. The relative contributions are attributed to non-linear, correlated assumptions on mass-transfer stability, angular-momentum loss, CE efficiency, and supernova physics.

Significance. If the compiled sample is representative, the result demonstrates that current population-synthesis frameworks permit a wide range of CE contributions for BBH/BHNS systems at comparable rates, underscoring the need for observables beyond merger rates and for transparent, reproducible channel definitions. The systematic taxonomy and cross-simulation aggregation constitute a useful organizational contribution.

major comments (2)
  1. [Abstract and compilation description] Abstract and compilation description: the central claim that BBH/BHNS channels span the full 0–100% CE range (with similar rates) is load-bearing on the assertion that the >200 simulations constitute an unbiased and sufficiently complete sampling of existing modeling frameworks; however, no explicit inclusion criteria, code-coverage statistics, or test for publication/availability bias are stated, leaving open the possibility that the observed degeneracy is an artifact of incomplete sampling rather than a robust feature of the model space.
  2. [Results on BNS versus BBH/BHNS contrast] Results on BNS versus BBH/BHNS contrast: the claim that BNS formation proceeds almost exclusively through CE channels (>90–100%) while BBH/BHNS do not is presented as qualitatively different, yet the manuscript provides no quantitative breakdown (e.g., by code family or by specific parameter assumptions) showing that this contrast survives when the same selection and taxonomy are applied uniformly across all three source types.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'more than 200' could be replaced by the exact count once the final compilation is fixed, and a one-sentence statement of the taxonomy structure would improve immediate clarity.
  2. [Notation] Notation: the distinction between 'with-CE' and 'without-CE' pathways is used throughout but is not given an explicit operational definition (e.g., whether a single CE phase suffices or whether both components must experience CE) until later in the text; an early boxed definition would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive report and recommendation for major revision. We address each major comment below and agree that clarifications on compilation methodology and additional quantitative breakdowns will strengthen the manuscript. We plan to incorporate these changes in the revised version.

read point-by-point responses

  1. Referee: [Abstract and compilation description] Abstract and compilation description: the central claim that BBH/BHNS channels span the full 0–100% CE range (with similar rates) is load-bearing on the assertion that the >200 simulations constitute an unbiased and sufficiently complete sampling of existing modeling frameworks; however, no explicit inclusion criteria, code-coverage statistics, or test for publication/availability bias are stated, leaving open the possibility that the observed degeneracy is an artifact of incomplete sampling rather than a robust feature of the model space.

    Authors: We acknowledge that the original manuscript did not include an explicit description of inclusion criteria or bias assessment for the compilation of >200 simulations. The sample was assembled from all published isolated-binary population-synthesis studies (post-2010) that report quantitative CE versus non-CE channel fractions for at least one compact-object merger type using standard codes. In the revision we will add a dedicated methods subsection specifying the literature search protocol, inclusion criteria, code coverage, and a discussion of potential publication/availability bias. We note that the 0–100% span for BBH/BHNS appears consistently across independent codes and parameter explorations, which argues against it being solely a sampling artifact, but we will make this explicit. revision: yes

  2. Referee: [Results on BNS versus BBH/BHNS contrast] Results on BNS versus BBH/BHNS contrast: the claim that BNS formation proceeds almost exclusively through CE channels (>90–100%) while BBH/BHNS do not is presented as qualitatively different, yet the manuscript provides no quantitative breakdown (e.g., by code family or by specific parameter assumptions) showing that this contrast survives when the same selection and taxonomy are applied uniformly across all three source types.

    Authors: We agree that the manuscript would benefit from explicit quantitative breakdowns to demonstrate the robustness of the BNS (>90–100% CE) versus BBH/BHNS (0–100%) contrast under uniform taxonomy. Although the aggregate results apply the same hierarchical channel definitions to all simulations, we did not stratify by code family or key assumptions in the submitted version. In the revision we will add supplementary tables and figures providing these breakdowns (e.g., CE-fraction distributions per source type, stratified by code and by assumptions on mass-transfer stability and CE efficiency) to confirm the contrast holds uniformly. revision: yes

Circularity Check

0 steps flagged

No circularity: result follows from external simulation compilation

full rationale

The paper's core claim (BBH/BHNS pathways span 0-100% CE contribution with rate degeneracy, while BNS are >90% CE) is obtained by systematically comparing >200 independent published population-synthesis runs. No internal equations, fitted parameters, or self-referential definitions are used to generate the spread or degeneracy; the result is a direct empirical observation of the existing literature ensemble. Self-citations, if present, are not load-bearing for the central degeneracy statement. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis depends on the assumption that existing population-synthesis codes collectively span the physically plausible range of outcomes and that the literature sample is representative; no new free parameters or invented entities are introduced.

axioms (1)
  • domain assumption The population-synthesis simulations used in the compilation accurately capture the dominant binary-evolution physics under the assumptions of each code.
    Invoked when treating the spread of reported CE fractions as representative of possible formation pathways.

pith-pipeline@v0.9.1-grok · 5917 in / 1377 out tokens · 47547 ms · 2026-06-28T04:42:35.760559+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

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

  1. Lower Your Rates: On Claims of a Binary Black Hole Merger-Rate Crisis

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    A meta-analysis of 1490 BBH merger rate predictions from 57 studies shows substantial subsets reproduce or underestimate the observed rate, indicating that apparent crises are model-dependent rather than universal.

  2. Twin Peaks: Resolving Features in the Binary Black Hole Mass Function with COSMIC-METISSE

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Reference graph

Works this paper leans on

14 extracted references · 1 canonical work pages · cited by 2 Pith papers

  1. [1]

    Compact object mergers: exploring uncertainties from stellar and binary evolution with SEVN

    Abrams N. S., et al., 2025, ApJS, 276, 10 Agrawal P., Hurley J., Stevenson S., Rodriguez C. L., Szécsi D., Kemp A., 2023, MNRAS, 525, 933 Alvarez-Lopez S., Heinzel J., Mould M., Vitale S., 2025, arXiv e-prints, p. arXiv:2506.20731 Andreoni I., et al., 2020, ApJ, 904, 155 Andrews J. J., Farr W. M., Kalogera V., Willems B., 2015, ApJ, 801, 32 Andrews J. J.,...

    work page doi:10.5281/zenodo.20494714 2025

  2. [2]

    other” do undergo a CE episode (but, for example, do not undergo SMT prior to the first SN hence the ‘other’ classification). Accordingly, we as- sign these systems to the “with CE

    Intotal, thisyields15distinctBBHmerger-rateestimatesand their corresponding CE and SMT contributions. Boesky et al. (2024b,a) [Bo24]—Boesky et al. (2024a,a) use theCOMPASpopulationsynthesiscodetocompute21model variations: 12 exploring different values of the CE efficiency parameter (𝛼) and binding energy parameter (𝛽), and 9 vary- ing the remnant mass pre...

    2023

  3. [3]

    with CE” category, and classify the remaining systems as “without CE

    to the “with CE” category, and classify the remaining systems as “without CE”. For the Level 2 classification, we adopt the authors’moredetailedtaxonomy,whichdistinguishessystems according to whether CE, SMT, or no mass transfer occurs in the primary and/or secondary component. We obtain the to- tal BBH merger rate for the fiducial model from Table 1 of B...

    2023

  4. [4]

    with CE” group and classify all remaining systems as “with- out CE

    We adopt these definitions for our Level 2 classification. For the Level1categorization,wecombinethethreeCE-relatedchan- nels (classic, single-core, and double-core CE) into a single “with CE” group and classify all remaining systems as “with- out CE”. 6 https://github.com/FloorBroekgaarden/DCO_FormationChannels Dorozsmai & Toonen (2024) [DT22]—Dorozsmai ...

    2024

  5. [5]

    MT switch

    Li et al. (2025a) [Li25]—Li et al. (2025a) study the formation channels,massdistributions,andmergerratesofBBHsystems using the binary population-synthesis codeMOBSE, explic- itly incorporating chemically homogeneous evolution (CHE) alongside the more traditional CE and SMT isolated-binary evolutionpathways. Theauthorsexploreagridofpopulation- synthesis mo...

    2021

  6. [6]

    Weretrievetheirformationchannel rates from digitizing Figure 6, which shows the contributions of the formation channels to the BBH merger rate

    based on only stable mass transfer, the classic CE channel, and the single-core CE and double-coreCEchannels. Weretrievetheirformationchannel rates from digitizing Figure 6, which shows the contributions of the formation channels to the BBH merger rate. We take therateatredshift𝑧∼0usingaplotdigitizer. Notethatinthe FigureitisclearthattheclassicCEchanneldo...

    2015

  7. [7]

    conventional

    Across their broad model variations—including changes in𝛼 CE, chemically homogeneous evolution, supernova natal kicks, remnant-mass prescriptions, and envelope binding en- ergies—theyfindarobustandconsistentresult: BNSmergers form exclusively through channels involving at least one CE phase. In contrast, BHNS and BBH systems exhibit a strong dependence on...

    2018

  8. [8]

    andincludeinFigures14and15. TheirresultsshowthatBNS systems form almost exclusively through channels involving a CE phase across all metallicities, BHNS systems are pre- dominantly formed via CE channels, and BBH systems can receive a substantial contribution from channels without CE, including CHE. We do not include this study in our main ta- blesandfigu...

    2018

  9. [9]

    This limits a consistent comparison with studies that explore metallicity-dependent trends and report quantitative channel contributions

    We do not include this study in our formation-channel comparison, as it is restricted to a single (solar) metallicity and does not provide channel frac- tions for intrinsic merger rates across a broader model grid. This limits a consistent comparison with studies that explore metallicity-dependent trends and report quantitative channel contributions. We i...

    2020

  10. [10]

    In the𝑞c formalism, mass transfer becomes dynamically unstable when the donor- to-accretor mass ratio exceeds a threshold value, leading to a CE phase

    with response coefficients such as the adiabatic mass– radiusexponent𝜉≡d ln𝑅/d ln𝑀(e.g.𝜉 ad,rad inDorozsmai& Toonen (2024) for radiative envelopes). In the𝑞c formalism, mass transfer becomes dynamically unstable when the donor- to-accretor mass ratio exceeds a threshold value, leading to a CE phase. In contrast,𝜉-based prescriptions compare the donor’s ra...

    2024

  11. [11]

    Used in Olejak et al

    This highly permissive criterion substantially expands the parameter space in which binaries avoid CE evolution. Used in Olejak et al. (2021) (OL21; their model M480.B), which addi- tionally uses the Pavlovskii et al. (2017a) donor-radius gridtodeterminestabilityacrossarangeofmassesand compact-object accretors. The related label𝑞c <8CE switchrefers to mod...

    2021

  12. [12]

    2021, for both exceptions)

    and BPASS(BRI22;Eldridgeetal.2017),whichbothavoidafixed threshold:POSYDONinterpolates pre-computedMESAbi- nary grids that self-consistently capture the donor response as a function of mass, mass ratio, separation, and metallicity, whileBPASSruns detailedSTARSmodels for each individ- ual system (see footnote 2 of Bavera et al. 2021, for both exceptions). T...

    2017

  13. [13]

    log𝑈prior

    noMTZAMS(suppressedmasstransferatzero-agemainsequence) —ThelabelnoMTZAMS(appearinginBA21rows)refersto amodelvariantinwhichmasstransferatorverynearthezero- age main sequence — typically arising from contact or over- contact systems — is suppressed. In the default Bavera et al. (2021) framework, such systems are allowed to undergo mass transfer and potentia...

    2021

  14. [14]

    For BBH and BHNS mergers, the formation-channel frac- tions show substantially more variation across models and metallicity. For BBH systems in particular, the relative con- tribution of without-CE channels generally increases toward the lowest metallicities (log10 (𝑍)≲−2.5), likely reflecting the reduced stellar wind mass loss and the resulting larger st...

    2019