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

Israel); Lotem Unger; Noam Soker (Technion

REVIEW 2 major objections 1 minor 300 references

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

T0 review · 2 major / 1 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read A triple-star channel with two common envelope phases produces merging binary black holes that match the observed effective spin distribution.

desk verdict The paper proposes a two-CEE triple channel to explain BBH χ_eff but assumes the key spin alignments without any calculation or citation to back them up. read the letter →

arxiv 2606.27193 v1 pith:GGILMO2M submitted 2026-06-25 astro-ph.HE

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

classification astro-ph.HE

keywords binaryblackholescommonenvelopeevolutiontriplestarsystemsgravitationalwavesourcesholespinscorecollapsesupernovaestellar

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

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.

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.

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.

Watch

Extended reading notes

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

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.

Editorial extensions

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.

Reading between the lines

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

read the letter

The main thing to know is that this paper offers a concrete triple-star channel using two common-envelope phases to produce merging black holes with a positive average χ_eff and a negative tail. It is new in laying out how the first CEE phase could set the first black hole spin along an inclined inner orbit while the second aligns with the final binary orbit.

The rate comparison is the part that holds up best. The authors take empirical initial distributions for triples, apply a hierarchical stability condition, and show the predicted merging BBH to core-collapse supernova ratio can reach up to twice the observed value. That calculation is transparent and uses real numbers rather than free parameters.

The soft spot is the spin alignment. The text states that the tertiary spirals in and spins up the core so the first black hole ends up aligned with the inner binary, while the second black hole aligns with the final orbit. No hydrodynamical result, no simulation reference, and no parameter study is given to show this actually happens for the relevant masses and separations. If the spins instead follow a broader distribution, both the positive mean and the negative tail go away, independent of the rate numbers.

This is for people working on black hole binary formation channels and the χ_eff puzzle in gravitational-wave data. A reader tracking alternative routes to the observed spin distribution would get a specific proposal to test.

It deserves peer review. The rate work is checkable and the channel is distinct enough that referees can ask for the missing support on the alignments.

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)

[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.
[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)

[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

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
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 · score 0.0 of 10

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.

Assumptions & free parameters 1 free parameters · 1 assumptions · 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.

assumptions (1)

domain assumption hierarchical stability criterion
Imposed to select stable triple configurations from the initial distributions.

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Cite this review

Pith. "Pith review of Stellar black hole binaries from two common envelope evolution phases in triple stellar systems." pith.science (2026). https://pith.science/paper/GGILMO2M

@misc{pith2026260627193,
  author       = {Pith},
  title        = {Pith review of: Stellar black hole binaries from two common envelope evolution phases in triple stellar systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GGILMO2M}},
  note         = {Machine review of arXiv:2606.27193}
}

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.

Figures

Figures reproduced from arXiv: 2606.27193 by the authors.

**Figure 1.** Distribution of the effective spin parameter, χeff , for 256 BBH events from the O1–O4b observing runs. Asymmetric alignment is observed, with 164 systems possessing positive effective spins (χeff > 0, green), 81 systems displaying 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 mean (⟨χeff… view at source ↗

**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 evolution of the secondary star through the second CEE and second CCSN, resulting in a… view at source ↗

**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; this angle… view at source ↗

Figures from the paper (4 more)

**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 dynamical stability filter applied only to triple systems. The observed CCSN and BBH merger rates are us…

**Figure 5.** Figure 5: Probability density of dynamically stable hierarchical 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]. T…

**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.…

**Figure 7.** Figure 7: Simulated justification of the adopted inner-orbit 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 …

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Pith tools

Reviewed June 26, 2026 · model on record in the stance chip above.

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