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arxiv: 2606.28506 · v1 · pith:M3PJVYVZnew · submitted 2026-06-26 · 🌌 astro-ph.HE

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

Duncan B. Maclean , Poojan Agrawal , Katelyn Breivik , and Alexandra G. Guerrero , Michael Zevin , Mathieu Renzo , Carl L. Rodriguez This is my paper

Pith reviewed 2026-06-30 01:21 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords binary black holesgravitational wavesstellar evolutionmass ratio reversalpopulation synthesisconvective boundary mixingmerger ratesMESA tracks
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The pith

Binary black hole primary masses show twin peaks near 8 and 13 solar masses in most model variations, with the higher peak from mass ratio reversal.

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

The paper generates new MESA stellar evolution tracks across a range of metallicities while varying wind mass loss and convective boundary mixing, then interpolates them with METISSE into the COSMIC binary population synthesis code to produce local-universe merging binary black hole populations. It reports that the primary mass spectrum reaches a maximum near 10 solar masses that typically splits into sub-populations at 8 and 13 solar masses, the higher one dominated by systems whose progenitors reversed mass ratio. The split, the associated anticorrelation between primary mass and mass ratio, and the overall merger rate all shift when the two stellar-physics parameters are changed, with convective boundary mixing producing the largest effect.

Core claim

We find a maximum in the primary mass spectrum near 10M_⊙ which in most model variations is composed of two sub-populations at ≈8M_⊙ and ≈13 M_⊙, with the higher-mass population dominated by BBHs whose progenitors underwent a mass ratio reversal (MRR). This population also suggests an anticorrelation between higher primary masses and mass ratio, as BBHs with m1≳10M_⊙ preferentially undergo MRR and prefer a final mass ratio of q≈0.7. Variations in our stellar tracks, especially CBM, lead to a factor of ≈6 difference in the rate, primarily due to modulation of the common envelope formation channel.

What carries the argument

Mass ratio reversal (MRR) in isolated binary evolution, which produces the higher-mass sub-population near 13 solar masses and drives the anticorrelation with final mass ratio.

If this is right

  • BBHs with primary masses above 10 solar masses preferentially end with mass ratios near 0.7 after mass ratio reversal.
  • Adjusting wind mass loss and convective boundary mixing can merge the two sub-populations into one peak near 9 solar masses.
  • Merger rates differ by a factor of approximately 6 across the grid, driven mainly by changes in the common-envelope channel.
  • The higher-mass sub-population arises almost entirely from progenitors that experienced mass ratio reversal.

Where Pith is reading between the lines

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

  • If future gravitational-wave catalogs resolve the two peaks, that would directly constrain how often mass ratio reversal occurs in massive binaries.
  • The strong sensitivity to convective boundary mixing points to a need for tighter observational or theoretical limits on that process before rates can be predicted reliably.
  • Because the rate variation is tied to common-envelope formation, independent constraints on common-envelope efficiency would test whether the modeled factor-of-six spread is realistic.

Load-bearing premise

Isolated binary evolution with the COSMIC code and the chosen MESA tracks, after varying only wind mass loss and convective boundary mixing, captures the dominant channel for merging binary black holes.

What would settle it

A catalog of hundreds of gravitational-wave events whose primary-mass distribution shows only a single peak near 9-10 solar masses, with no resolved sub-structure at 8 and 13 solar masses, would falsify the claim that the twin peaks appear in most model variations.

Figures

Figures reproduced from arXiv: 2606.28506 by and Alexandra G. Guerrero, Carl L. Rodriguez, Duncan B. Maclean, Katelyn Breivik, Mathieu Renzo, Michael Zevin, Poojan Agrawal.

Figure 1
Figure 1. Figure 1: Stellar tracks interpolated with COSMIC-METISSE for a 25 M⊙ star, obtained from tracks using each of our stellar grid variations. The dashed line shows a 25 M⊙ track produced by SSE (O. R. Pols et al. 1998; J. R. Hurley et al. 2000). Post-main-sequence behavior differs significantly in each model, and the divergence between tracks correlates with increasing birth metallicity. At solar-like (Z = 0.014, righ… view at source ↗
Figure 2
Figure 2. Figure 2: The maximum radii of stellar tracks for 10.0 ≤ mZAMS/M⊙ ≤ 150.0 interpolated with COSMIC-METISSE. Maximum radii calculated with METISSE diverge sharply from the SSE fitting formulae, which are extrapolated at masses greater than 50 M⊙. The radial growth of stars in each model shows strong mass and metallicity dependence, but we do observe several trends. At low metallicity, the CBM implementation is the do… view at source ↗
Figure 3
Figure 3. Figure 3: A schematic representation of our population synthesis pipeline and the uncertainties associated with each step. Stellar tracks evolved with MESA (left) provide us with stellar parameters for a given ZAMS mass, time, and metallicity. METISSE (middle) interpolates between these tracks to enable continuous sampling in mass. COSMIC (right) then samples the full population of initial masses, orbital periods, a… view at source ↗
Figure 4
Figure 4. Figure 4: The volumetric BBH merger rate as a function of redshift. The LVK PixelPop posterior is given in grey, and the shaded region denotes the 90% CI. Our SSE refer￾ence model is given by the dashed line. Our standard and new winds models intersect the median LVK rate estimate at z ⪅ 0.2. The new CBM, new winds & CBM, and SSE, models better trace the redshift-dependent star formation history (dot-dashed black li… view at source ↗
Figure 5
Figure 5. Figure 5: The differential BBH merger rate as a function of m1 (left) and of q ≡ m2/m1 (right). These distributions include binaries merging at z < 0.2, as calculated with Equation 8. We include the SSE model (dashed) and the LVK PixelPop posterior (shaded 90% CI) for reference ( LIGO Scientific Collaboration et al. 2026b). Note the twin features at m1 ≈ 8M⊙ and ≈ 13M⊙, which approximately flank the LVK peak at 10M⊙… view at source ↗
Figure 6
Figure 6. Figure 6: Differential BBH merger rates as a function of m1 and q for each of our models, split by whether a BBH undergoes MRR. We also show the LVK PixelPop posterior for reference ( LIGO Scientific Collaboration et al. 2026b). BBHs which experience MRR preferentially form with primary masses > 10M⊙, forming the bulk of the MRR (≈ 13M⊙) peak in our results. MRR is also strongly associated with mass ratios ∼ 0.7, a … view at source ↗
Figure 7
Figure 7. Figure 7: The normalized differential merger rate density parameterized by the ZAMS mass ratio, qZAMS, and the logarithm of the ZAMS period, log (PZAMS). The contour lines denote BBHs which do and do not undergo MRR (90th percentile regions). Systems with a natal mass ratio ≳ 0.5 are likely to experience MRR and to form BBHs with m1 ≳ 10M⊙. Systems with more unequal mass ratios are unlikely to experience MRR and mor… view at source ↗
Figure 8
Figure 8. Figure 8: Differential merger rates as a function of m1 (left set) and of q (right set) colored according to the mass transfer case of the initial mass transfer episode. In all models, binaries which undergo Case A mass transfer preferentially form BBHs with primary masses m1 ≥ 10M⊙ and mass ratios q ≳ 0.6. Binaries which undergo Case B mass transfer produce a prominent peak at m1 ≈ 8M⊙. In our standard and new wind… view at source ↗
Figure 9
Figure 9. Figure 9: The normalized BBH merger rate density in m1, q space for each of our model variations (columns) and βacc variations (rows). Our fiducial, thermally-limited models occupy the final row. The 90th percentile regions of non-MRR and MRR systems are denoted by dash-dotted lines. These contoured regions reveal two distinct populations flanking the 10M⊙ peak. MRR is strongly linked with the higher-mass (m1 ≈ 13M⊙… view at source ↗
Figure 10
Figure 10. Figure 10: The differential BBH merger rate at z < 0.2 as a function of metallicity for each of our models, subdivided into binaries which undergo only stable mass transfer (center) and those which undergo at least one CE (bottom). BBHs in stable mass transfer-dominated models (standard, new winds) form primarily from ≤ 1%Z⊙. The CE-dominated models (new CBM, new winds & CBM) draw mergers from across the metallicity… view at source ↗
Figure 11
Figure 11. Figure 11: The differential BBH merger rate for our new winds & CBM model variation, split by birth metallicity. Un￾surprisingly, we observe a negative correlation between the metallicity and the primary mass. This model variation uniquely produces a single peak at ≈ 8−9M⊙. It also produces a sub-population of high metallicity BBHs at Z ≥ Z⊙ (≥ 0.014) clustered around the 10M⊙ LVK PixelPop maximum ( LIGO Scientific … view at source ↗
Figure 12
Figure 12. Figure 12: The BBH merger rate (left) primary mass distribution (center), and mass ratio distribution (right) for a hypothetical, normalized new winds & CBM model. We scaled our model by a factor of ≊ 4.487−1 , such that the BBH merger rate equals the LVK PixelPop ( LIGO Scientific Collaboration et al. 2026b) rate at z = 0.02. This demonstrative model shows notable agreement in the redshift evolution of the merger r… view at source ↗
read the original abstract

Gravitational waves from inspiraling binary black holes (BBHs) provide insights into the lives and deaths of massive stars. Population synthesis allows us to model these binaries through isolated binary evolution, but its predictive power is limited by difficulties in varying the stellar models and their associated uncertainties. We present a new grid of stellar tracks computed with the open-source stellar evolution code MESA, spanning metallicities $10^{-3} \le Z/Z_{\odot} \le 7$. We vary two stellar physics parameters: wind-driven mass loss and the convective boundary mixing (CBM) mechanism. We pair these models with the Method of Interpolation for Single Stellar Evolution (METISSE) and binary population synthesis code COSMIC to obtain synthetic populations of merging BBHs in the local Universe. We find a maximum in the primary mass spectrum near $10M_\odot$ which in most model variations is composed of two sub-populations at $\approx8M_{\odot}$ and $\approx13 M_\odot$, with the higher-mass population dominated by BBHs whose progenitors underwent a mass ratio reversal (MRR). This population also suggests an anticorrelation between higher primary masses and mass ratio, as BBHs with $m_1\gtrapprox10M_\odot$ preferentially undergo MRR and prefer a final mass ratio of $q\approx0.7$. However, the location and relative strength of these two sub-populations is sensitive to our assumed stellar physics: varying both the wind and CBM treatments can merge the MRR and non-MRR populations into a single peak near $9M_\odot$. Variations in our stellar tracks, especially CBM, lead to a factor of $\approx6$ difference in the rate, primarily due to modulation of the common envelope formation channel.

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 paper computes a new grid of MESA stellar evolution tracks at metallicities 10^{-3} ≤ Z/Z_⊙ ≤ 7, varying wind-driven mass loss and convective boundary mixing (CBM). These tracks are interpolated via METISSE and fed into the COSMIC binary population synthesis code to generate synthetic merging BBH populations. The central result is a primary-mass maximum near 10 M_⊙ that, in most explored model variations, splits into sub-populations at ≈8 M_⊙ and ≈13 M_⊙, with the higher-mass peak dominated by systems whose progenitors experienced mass-ratio reversal (MRR); the work also reports an anticorrelation between primary mass and mass ratio for m1 ≳ 10 M_⊙ and a factor-of-≈6 variation in merger rate driven primarily by CBM.

Significance. If the reported twin-peak structure and its MRR association survive broader exploration of binary-physics parameters, the result would provide a concrete, falsifiable link between stellar-evolution uncertainties and features in the GW-observable BBH mass function, offering a potential observational handle on CBM and wind prescriptions.

major comments (2)
  1. [Abstract] Abstract: the statement that the ≈13 M_⊙ sub-population is 'dominated by BBHs whose progenitors underwent a mass ratio reversal' is presented as a load-bearing interpretive claim, yet the manuscript provides neither the numerical fraction of MRR systems in each sub-population nor the precise algorithmic definition used to tag MRR events in the COSMIC output.
  2. [Abstract] Abstract and model-description section: the claim that the twin-peak feature appears 'in most model variations' rests on the assumption that the two varied parameters (wind scaling and CBM efficiency) plus the fixed COSMIC settings (including α_CE and supernova kicks) are sufficient to establish robustness; the abstract itself shows that CBM variations alone can erase the split, but no tests of other COSMIC knobs are reported, leaving open whether the MRR-driven feature is generic or an artifact of the default binary-physics choices.
minor comments (2)
  1. [Abstract] The abstract refers to 'the rate' without specifying whether this is the local merger rate density, the number of systems per unit star-forming mass, or a normalized quantity; a brief clarification of the normalization would aid comparison with other population-synthesis studies.
  2. [Abstract] Notation for mass ratio q is introduced without an explicit definition in the abstract; while conventional, a parenthetical reminder (q = m2/m1) would remove any ambiguity when discussing the reported anticorrelation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive comments on our manuscript. We respond point-by-point to the major comments below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that the ≈13 M_⊙ sub-population is 'dominated by BBHs whose progenitors underwent a mass ratio reversal' is presented as a load-bearing interpretive claim, yet the manuscript provides neither the numerical fraction of MRR systems in each sub-population nor the precise algorithmic definition used to tag MRR events in the COSMIC output.

    Authors: We agree that explicit fractions and a precise definition of the MRR tagging algorithm would strengthen the presentation. In the revised manuscript we will add both: a description of how MRR systems are identified from the COSMIC output (initially less-massive star becomes the more massive BH after mass transfer) and the numerical fractions of MRR versus non-MRR systems within each sub-population. These additions will appear in the results section and be referenced from the abstract. revision: yes

  2. Referee: [Abstract] Abstract and model-description section: the claim that the twin-peak feature appears 'in most model variations' rests on the assumption that the two varied parameters (wind scaling and CBM efficiency) plus the fixed COSMIC settings (including α_CE and supernova kicks) are sufficient to establish robustness; the abstract itself shows that CBM variations alone can erase the split, but no tests of other COSMIC knobs are reported, leaving open whether the MRR-driven feature is generic or an artifact of the default binary-physics choices.

    Authors: The referee is correct that our parameter exploration is restricted to stellar-evolution inputs while binary-physics settings remain at COSMIC defaults. The abstract already notes sensitivity to CBM. We will revise the abstract and model-description section to state explicitly that the twin-peak structure is recovered in most of the stellar-physics variations we explored, while clarifying that we do not claim robustness against changes in binary parameters such as α_CE or kick velocities. We will add a brief recommendation for future work on those parameters. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forward simulation results independent of inputs

full rationale

The paper reports numerical outcomes from COSMIC-METISSE population synthesis runs on a new MESA grid with two explicitly varied stellar parameters (wind mass loss, CBM). The twin-peak structure near 10 M⊙, sub-populations at ≈8 and ≈13 M⊙, MRR dominance, and rate variations are direct outputs of these forward models. No equations, fitted parameters, or self-citations reduce the reported mass-function features or rates to quantities defined by the same data or prior author work. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the isolated-binary channel assumption and on the chosen stellar-physics variations being representative; no new particles or forces are introduced.

free parameters (2)
  • wind-driven mass loss scaling factor
    Explicitly varied across the grid to explore uncertainty; specific values not listed in abstract.
  • convective boundary mixing efficiency parameter
    Explicitly varied across the grid to explore uncertainty; specific values not listed in abstract.
axioms (2)
  • domain assumption Isolated binary evolution dominates the local merging BBH population
    The study employs COSMIC for isolated binaries without including dynamical channels.
  • domain assumption MESA models with the chosen wind and CBM prescriptions adequately represent real massive-star evolution
    The grid is built on this premise and the results are interpreted as physical.

pith-pipeline@v0.9.1-grok · 5889 in / 1542 out tokens · 50195 ms · 2026-06-30T01:21:04.443770+00:00 · methodology

discussion (0)

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