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arxiv: 2606.27193 · v1 · pith:GGILMO2Mnew · submitted 2026-06-25 · 🌌 astro-ph.HE

Stellar black hole binaries from two common envelope evolution phases in triple stellar systems

Lotem Unger , Noam Soker (Technion , Israel) This is my paper

Pith reviewed 2026-06-26 03:18 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords binary black holescommon envelope evolutiontriple star systemsgravitational wave sourcesblack hole spinscore collapse supernovaestellar binary evolution
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The pith

A triple-star channel with two common envelope phases produces merging binary black holes that match the observed effective spin distribution.

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

The paper proposes that some close binary black holes arise in hierarchical triple systems through two successive common envelope phases. In the first phase a massive star engulfs a low-mass companion while the tertiary star spirals inward and spins up the core; the core later collapses to the first black hole whose spin follows the inner binary orbit, which can be inclined to the outer orbit. In the second phase the remaining massive star engulfs the first black hole, forms the second black hole, and the final binary has one spin that can be misaligned and one that is more aligned with the orbital plane. This geometry yields an average positive effective inspiral spin with a tail of negative values. The calculated formation rate reaches up to twice the observed rate of merging black hole binaries relative to core-collapse supernovae, indicating the channel can supply a substantial fraction of the detected population.

Core claim

We propose a triple-star evolutionary channel involving two common envelope evolution (CEE) phases to form close binary black hole (BBH) systems with an average positive effective inspiral spin χ_eff and a tail of systems having χ_eff<0. The first BH progenitor engulfs a low-mass star during the post-main-sequence evolution. The tertiary star spirals in and spins up the core, which forms the first BH at the first core-collapse supernova (CCSN) explosion. Its spin is along the orbital angular momentum of the inner binary, which can be highly inclined to the outer binary angular momentum. The secondary star later engulfs the BH in a second CEE phase and explodes as a CCSN to form the second BH

What carries the argument

The two successive common envelope phases in a hierarchical triple, in which the first phase sets the first black hole spin along the inclined inner orbit while the second phase sets the second black hole spin closer to the final binary orbit.

If this is right

  • The channel can account for a substantial share of the merging binary black holes detected by gravitational-wave observatories.
  • It produces a population whose effective spins are on average positive yet include a negative tail without fine-tuning.
  • The first black hole spin remains misaligned with the final orbit while the second black hole spin is more aligned.
  • The formation efficiency reaches up to twice the observed merging rate relative to core-collapse supernovae.

Where Pith is reading between the lines

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

  • Future catalogs with better spin measurements could quantify how large a fraction of events arise from this triple channel versus isolated binary evolution.
  • The same geometry may operate in other compact-object binaries formed inside triples, such as neutron-star black-hole systems.
  • The required initial triple distributions and stability criteria can be tested against upcoming large-scale stellar surveys.

Load-bearing premise

The tertiary star spirals in during the first common envelope phase and spins up the core so that the first black hole spin aligns with the inner binary angular momentum, which is often inclined relative to the outer binary.

What would settle it

A measured fraction of merging binary black holes with negative effective spin that lies well outside the range produced by this channel, or an observed merging rate that exceeds twice the core-collapse supernova rate after accounting for selection effects.

Figures

Figures reproduced from arXiv: 2606.27193 by Israel), Lotem Unger, Noam Soker (Technion.

Figure 1
Figure 1. Figure 1: Distribution of the effective spin parameter, χeff , for 256 BBH events from the O1–O4b observing runs. Asym￾metric alignment is observed, with 164 systems possessing positive effective spins (χeff > 0, green), 81 systems display￾ing negative spins (χeff < 0, red) and the 11 systems have zero effective spins (χeff = 0). The dashed vertical line marks the zero-point, and the black arrow denotes the sample m… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic evolutionary pathway of a hierarchical triple system leading to the formation of a merging BBH. The left column follows the primary star from the ZAMS through the inner CEE, the inner merger (tidal disruption of the tertiary), and the first CCSN, which produces the first-born BH. The right column follows the subsequent evo￾lution of the secondary star through the second CEE and sec￾ond CCSN, resu… view at source ↗
Figure 3
Figure 3. Figure 3: Schematic illustration of the angular momentum and spin configuration at four stages of the evolution described in section 2. (a) ZAMS: the inner orbital angular momentum L⃗ orb,in is inclined by an angle θ0 relative to the outer orbital angular momentum L⃗ orb. (b) Post first CCSN: the first-born BH carries a spin ⃗χ1 approximately aligned with L⃗ orb,in, and therefore inclined by θ13 relative to L⃗ orb; … view at source ↗
Figure 4
Figure 4. Figure 4: Schematic overview of the analytical calculation pipeline. Blue boxes indicate empirical inputs; green boxes indicate computational steps; the purple box marks the dy￾namical stability filter applied only to triple systems. The observed CCSN and BBH merger rates are used as external calibrations at the success fraction step. The final output is the inferred success fraction (or evolutionary efficiency fac￾… view at source ↗
Figure 5
Figure 5. Figure 5: Probability density of dynamically stable hi￾erarchical triples in the (log Pin, log Pout) plane at ZAMS. The orbital period P is reported in days. The light blue rectangle marking the adopted (log Pin, log Pout) range: log Pin ∈ [0.7, 1.5] and log Pout ∈ [2.3, 3.5]. The color scale shows the number of dynamically stable Monte Carlo sam￾ples per bin, out of 500,000 systems drawn from the Moe & Di Stefano (… view at source ↗
Figure 6
Figure 6. Figure 6: Initial ZAMS property distributions for binary systems that evolve into merging BBHs. The data was extracted from the compas population synthesis simulations by Grichener (2023). These distributions serve as a guide for constraining the initial parameters of our model. Left panel: ZAMS masses of the BH progenitors. Middle panel: initial mass ratio distribution, qZAMS ≡ M2,ZAMS/M1,ZAMS that leads to BBH mer… view at source ↗
Figure 7
Figure 7. Figure 7: Simulated justification of the adopted inner-or￾bit period range log(Pin/day) ∈ [0.7, 1.5] from two MSE runs. The first run samples log(Pin/day) within [0.5, 1.4] and the second run samples log(Pin/day) within [0.7, 1.6] (days), overall N = 630. Panel (a): fraction of systems per 0.1-dex bin that initiate the inner CEE, in which the primary engulfs and tidally destroys the tertiary. Panel (b): fraction tha… view at source ↗
read the original abstract

We propose a triple-star evolutionary channel involving two common envelope evolution (CEE) phases to form close binary black hole (BBH) systems with an average positive effective inspiral spin $\chi_{\rm eff}$ and a tail of systems having $\chi_{\rm eff}<0$, as observed by gravitational wave detectors. $\chi_{\rm eff}$ is the mass-weighted spin of the two merging BHs, and a positive (negative) value is for an effective spin along (opposite) the orbital angular momentum. The first BH progenitor engulfs a low-mass star during the post-main-sequence evolution. The tertiary star spirals in and spins up the core, which forms the first BH at the first core-collapse supernova (CCSN) explosion. Its spin is along the orbital angular momentum of the inner binary, which can be highly inclined to the outer binary angular momentum. The secondary star later engulfs the BH in a second CEE phase and explodes as a CCSN to form the second BH with a spin that is more aligned with the orbital angular momentum of the two BHs. We use empirically calibrated initial distributions of triple-star systems consisting of two massive stars and impose a hierarchical stability criterion. We compare the predicted ratio of merging BBHs to CCSN explosion rates and find it is up to a factor of 2 larger than the observed rate. This channel can significantly contribute to the population of observed merging BBHs and can explain their qualitative spin distribution.

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 / 1 minor

Summary. The manuscript proposes a triple-star evolutionary channel involving two common envelope evolution (CEE) phases to form close binary black hole (BBH) systems. It claims this produces merging BBHs with an average positive effective inspiral spin χ_eff and a tail of negative χ_eff values, matching gravitational-wave observations. Using empirically calibrated initial distributions of triple systems and a hierarchical stability criterion, the predicted ratio of merging BBHs to core-collapse supernova (CCSN) rates is up to a factor of 2 larger than observed, suggesting the channel can significantly contribute to the observed population and explain the qualitative spin distribution.

Significance. If the spin-alignment assumptions hold, the channel provides a geometric explanation for the observed χ_eff distribution via the two CEE phases without additional tuning. The rate comparison, based on empirical initial distributions, indicates competitiveness with other channels. Strengths include the direct use of observed triple-star distributions and the falsifiable prediction for both rate and spin properties.

major comments (2)
  1. [Abstract and model description] Abstract and § on spin evolution: The assumption that the tertiary star's spiral-in during the first CEE spins up the core such that the first BH spin aligns with the inner binary orbital angular momentum (inclined to the outer binary) is stated without hydrodynamical results, parameter studies for the relevant mass ratios/separations, or citations to supporting simulations. This alignment is load-bearing for the claim of both positive mean χ_eff and negative tail; if the first-BH spin direction is instead drawn from a broader distribution, the mechanism for the qualitative spin distribution collapses independent of the rate comparison.
  2. [Rate comparison] Rate comparison section: The claim that the predicted merging BBH to CCSN rate ratio is up to a factor of 2 larger than observed depends on the specific implementation of the hierarchical stability criterion, common-envelope efficiency, and selection of merging systems; without quantitative details or sensitivity tests on these, it is unclear whether the factor-of-2 comparison robustly supports the 'significantly contribute' conclusion.
minor comments (1)
  1. [Abstract] Notation for χ_eff should be defined at first use with explicit reference to the standard LIGO/Virgo definition (mass-weighted sum of spin components along orbital angular momentum).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments, which have helped us improve the clarity and robustness of our manuscript. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and model description] Abstract and § on spin evolution: The assumption that the tertiary star's spiral-in during the first CEE spins up the core such that the first BH spin aligns with the inner binary orbital angular momentum (inclined to the outer binary) is stated without hydrodynamical results, parameter studies for the relevant mass ratios/separations, or citations to supporting simulations. This alignment is load-bearing for the claim of both positive mean χ_eff and negative tail; if the first-BH spin direction is instead drawn from a broader distribution, the mechanism for the qualitative spin distribution collapses independent of the rate comparison.

    Authors: We acknowledge that the alignment of the first BH spin with the inner binary orbital angular momentum is presented as a model assumption without new hydrodynamical simulations or dedicated parameter studies in this manuscript. This assumption follows from the expectation that angular momentum transfer during the tertiary's spiral-in in the first CEE phase aligns the core spin with the inner orbit. We will revise the relevant sections to explicitly identify this as an assumption, cite existing literature on angular momentum transport in CEE, and add a short discussion of how a broader spin distribution would modify the predicted χ_eff distribution. Even under moderate deviations from perfect alignment, the geometric effect of the two successive CEE phases (inclining the inner binary relative to the outer orbit, followed by alignment of the second BH) continues to produce a positive mean χ_eff with a negative tail, preserving the qualitative match to observations. revision: partial

  2. Referee: [Rate comparison] Rate comparison section: The claim that the predicted merging BBH to CCSN rate ratio is up to a factor of 2 larger than observed depends on the specific implementation of the hierarchical stability criterion, common-envelope efficiency, and selection of merging systems; without quantitative details or sensitivity tests on these, it is unclear whether the factor-of-2 comparison robustly supports the 'significantly contribute' conclusion.

    Authors: We agree that additional quantitative details and sensitivity tests are required to demonstrate the robustness of the rate comparison. In the revised manuscript we will expand the rate section to specify the exact hierarchical stability criterion adopted, the value(s) chosen for the common-envelope efficiency parameter, and the precise criteria used to identify merging systems. We will also include sensitivity tests in which these parameters are varied over plausible ranges, showing that the predicted merging BBH to CCSN rate ratio remains within a factor of approximately two of the observed value across most of the explored parameter space. These additions will strengthen the conclusion that the channel can contribute significantly to the observed population. revision: yes

Circularity Check

0 steps flagged

No circularity: spin alignment is an explicit physical assumption, not a derived or fitted output

full rationale

The paper proposes a triple-star channel with two CEE phases and states the resulting spin alignments as direct physical consequences of the spiraling-in process (first BH spin along inner-binary orbit, second more aligned with final BBH orbit). These alignments are inputs to the qualitative spin-distribution claim rather than outputs derived from equations or data fits within the paper. Rate comparisons rely on empirically calibrated initial triple distributions and a hierarchical stability criterion, with no reduction of predictions to those inputs by construction. No self-citation load-bearing steps, ansatzes smuggled via citation, or uniqueness theorems appear in the provided text. The derivation chain is therefore self-contained; any weakness lies in the justification of the alignment assumption, not in circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on standard stellar evolution assumptions plus empirical calibrations for initial conditions and a stability criterion; no new entities are introduced.

free parameters (1)
  • initial distributions of triple-star systems
    Empirically calibrated distributions of triples consisting of two massive stars are used to generate the population.
axioms (1)
  • domain assumption hierarchical stability criterion
    Imposed to select stable triple configurations from the initial distributions.

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