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arxiv: 2604.10440 · v2 · submitted 2026-04-12 · 🌌 astro-ph.SR · astro-ph.HE

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A Path to Constraints on Common Envelope Ejection in Massive Binaries: Full Evolutionary Reconstruction of Three Black Hole X-ray Binaries

Zhenwei Li , Dandan Wei , Shi Jia , Hailiang Chen , Hongwei Ge , Zhuo Chen , Yangyang Zhang , Xuefei Chen
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Zhanwen Han
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Pith reviewed 2026-05-10 16:35 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.HE
keywords common envelopeblack hole X-ray binariesbinary evolutioncommon envelope efficiencynatal kicksmassive stars
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The pith

Reconstructing three black hole X-ray binaries requires common envelope ejection efficiencies above unity.

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

The paper reconstructs the evolutionary histories of three observed black hole X-ray binaries using binary evolution simulations and supernova modeling. It derives lower bounds on the common envelope efficiency parameter under different energy assumptions in the envelope. These bounds are all greater than one, with no successful paths below unity even in optimistic cases including enthalpy. This indicates that the standard common envelope formalism cannot explain the systems without extra energy or changes to the model. The work also finds that one binary required a large natal kick during its supernova.

Core claim

Through full evolutionary reconstruction of GRO J1655-40, SAX J1819.3-2525, and 4U 1543-47, the analysis establishes that self-consistent formation demands CE efficiency parameters satisfying α_0.5U ≳ 6.7, α_U ≳ 4.2 and α_H ≳ 1.7. No viable solutions exist with CE efficiencies below unity, even when envelope binding energy is reduced via enthalpy inclusion. This points to the necessity of additional energy sources or revision of the common envelope formalism itself. The formation of 4U 1543-47 specifically requires natal kicks of at least 50 km/s.

What carries the argument

The common envelope efficiency parameter α, which scales the orbital energy available to unbind the envelope, calculated under three cases: with half internal energy (α_0.5U), all internal energy (α_U), and including enthalpy (α_H).

If this is right

  • Standard isolated binary evolution cannot produce the observed systems without high CE efficiencies or extra energy.
  • The common envelope phase in massive binaries requires more energy than currently modeled.
  • One of the binaries, 4U 1543-47, must have received a substantial natal kick during the supernova.

Where Pith is reading between the lines

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

  • Similar high efficiencies might apply to other binaries, affecting gravitational wave merger rate predictions.
  • Dynamical formation channels could be more important if isolated evolution fails for these systems.
  • Additional observations of BHXBs could tighten constraints on efficiency parameters.

Load-bearing premise

The three observed black hole X-ray binaries formed exclusively via isolated binary evolution under the standard common envelope energy formalism.

What would settle it

Discovery of a formation pathway for any of these three systems that achieves the observed parameters with a CE efficiency below 1 using the standard formalism, or evidence that one system avoided the common envelope phase entirely.

Figures

Figures reproduced from arXiv: 2604.10440 by Dandan Wei, Hailiang Chen, Hongwei Ge, Shi Jia, Xuefei Chen, Yangyang Zhang, Zhanwen Han, Zhenwei Li, Zhuo Chen.

Figure 1
Figure 1. Figure 1: The typical evolutionary scenario for BH I/LMXBs. Abbreviations are as follows: ZAMS–zero-age main sequence, MT–mass transfer, CE–common envelope, He–helium, MS–main sequence, SN–supernova, BH–black hole, I/LMXB–intermediate-/low-mass X-ray binary. At stage 4, the dashed contour denotes the Roche lobe of the secondary star. Note that the successful ejection of the CE requires the secondary’s radius to be w… view at source ↗
Figure 2
Figure 2. Figure 2: Binding energy calculation example for a 34 M⊙ primary star. Panel (a): The evolutionary track in the HR diagram with the red cross indicating the specific evolution￾ary stage analyzed. The thick green line indicates that the star contains a He core. Panel (b): Radial profiles of hydro￾gen mass fraction (XH) and the sonic velocity Cs ≡ p P/ρ at this stage, where open circles mark the core-envelope bound￾ar… view at source ↗
Figure 3
Figure 3. Figure 3: presents a representative set of evolution￾ary tracks for GRO J1655, where we fix the initial BH mass at 5.1 M⊙ and the secondary mass at 3.8 M⊙ while varying the orbital period from 0.8 d to 2.4d in a step of 0.2 d. During the mass transfer phase, both the or￾bital periods and BH masses increase as the donor star loses mass. Among these models, the first seven bina￾ries (black dashed and red solid lines) … view at source ↗
Figure 4
Figure 4. Figure 4: Parameter spaces for GRO J1655. All marked bi￾naries can produce BHXBs consistent with GRO J1655’s ob￾served parameters. The viable parameter space consists of: colored solid circles representing allowable solutions where post-CE separations (Stage 4) satisfy R2 < R2,L, with colors indicating αH values (assuming a 34 M⊙ BH progenitor at R1 = 1000 R⊙); and open circles with crosses denoting for￾bidden grids… view at source ↗
Figure 6
Figure 6. Figure 6: Similar to [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: Similar to [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 8
Figure 8. Figure 8: The BH mass and companion star mass distri￾butions for the grid points shown in Figures 4-6. The up￾per panel distinguishes between the forbidden configurations (gray open circles with crosses) and viable systems when BH natal kicks are included (cyan circles). The middle and lower panels respectively display the allowable parameter space for systems excluding (red open circles) and including (cyan cir￾cle… view at source ↗
Figure 9
Figure 9. Figure 9: The influence of kick velocity on the CE effi￾ciency (αH). The chosen grid points for GRO J1655 and SAX J1819 are MBH = 5.1, M2 = 4.1 M⊙, Porb = 2.0 d, and MBH = 5.7, M2,i = 4.4 M⊙, Porb = 2.0 d, respectively. The BH progenitor is assumed to have an initial mass of 32 M⊙ with CE occurring when the progenitor reaches a stellar ra￾dius of 1000 R⊙. For the zero-kick case, the corresponding αH values are shown… view at source ↗
Figure 10
Figure 10. Figure 10: The minimum values of CE efficiency for GRO J1655 vary with the initial primary mass and the stellar radius. The left, middle and right panels correspond to the α0.5U, αU and αH cases respectively. The shaded gray region indicates CE efficiencies above the upper limit of the colorbar. Dashed lines indicate constant minimum CE efficiency values. Notably, when enthalpy is included (right panel), the minimum… view at source ↗
Figure 11
Figure 11. Figure 11: Similar to [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Similar to [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The minimum CE efficiencies required to form the three BHXBs. The red, black, and green sym￾bols correspond to the values of αH, αU, and α0.5U, re￾spectively. To simultaneously explain the formation of all three BHXBs, higher efficiency thresholds are required: α0.5U ≳ 6.7, αU ≳ 4.2, and αH ≳ 1.7. boundary. In this work, we adopt a physically motivated prescription, where the boundary is de￾termined by th… view at source ↗
Figure 14
Figure 14. Figure 14: The evolutionary tracks for GRO J1655 (left panels) and SAX J1819 (right panels) as functions of varying secondary masses, which are used to constrain the upper mass limits of the secondary stars. For GRO J1655, we adopt a mass cutoff of 5.0 M⊙, beyond which more massive secondaries cannot reproduce the observed effective temperature of the system. Similarly, for SAX J1819, we implement a cutoff at 6.2 M⊙… view at source ↗
Figure 15
Figure 15. Figure 15: The minimum CE efficiency requirements in the cases of 46 − 60 M⊙ BH progenitors for GRO J1655 [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The minimum CE efficiency requirements in the cases of 46 − 60 M⊙ BH progenitors for SAX J1819. B. THE CE EFFICIENCIES WITH MORE MASSIVE BH PROGENITORS In Figures 15-17, we present the minimum CE efficiency requirements for GRO J1655, SAX J1819, and 4U 1543, respectively, considering more massive BH progenitors. The results suggest systematically higher CE efficiency values compared to systems with lower-… view at source ↗
Figure 17
Figure 17. Figure 17: The minimum CE efficiency requirements in the cases of 46 − 60 M⊙ BH progenitors for 4U 1543 [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Minimum CE efficiencies as functions of initial BH progenitor masses for the three BHXBs. The open squares denote the corresponding minimum CE efficiency values previously shown in [PITH_FULL_IMAGE:figures/full_fig_p019_18.png] view at source ↗
read the original abstract

The massive binary common envelope (CE) phase plays a pivotal role in the formation of close black hole/neutron star (BH/NS) binaries, yet significant uncertainties remain in our understanding of this process. In this study, we aim to constrain the massive binary CE phase by systematically reconstructing three observed BH X-ray binaries (BHXBs): GRO J1655-40, SAX J1819.3-2525, and 4U 1543-47. Through comprehensive binary evolution simulations and parametric supernova (SN) modeling, we establish lower limits for the CE efficiency parameters under different energy considerations within the standard energy formalism. Specifically, we derive minimum values for three cases: $\alpha_{\rm 0.5U}$ and $\alpha_{\rm U}$ representing CE efficiencies with half and all of the internal energy contributing to the envelope ejection, respectively, and $\alpha_{\rm H}$ accounting for the envelope's enthalpy. Our analysis reveals that the self-consistent formation of these three BHXBs requires CE efficiency parameters satisfying: $\alpha_{\rm 0.5U}\gtrsim 6.7$, $\alpha_{\rm U}\gtrsim 4.2$ and $\alpha_{\rm H}\gtrsim 1.7$. Notably, we find no viable solutions with CE efficiency values below unity, even when considering the most extreme scenarios in which the envelope binding energy is significantly reduced through enthalpy inclusion. {Our results strongly imply that either additional energy sources are required, or the formalism itself must be revised.} Furthermore, we quantitatively assess the impact of BH natal kicks on our results. A key finding is that 4U 1543-47's formation requires substantial natal kicks ($\gtrsim 50 \;\rm km/s$), as lower kick velocities are incompatible with isolated binary evolution.

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

0 major / 0 minor

Summary. The manuscript performs full evolutionary reconstructions of three observed black hole X-ray binaries (GRO J1655-40, SAX J1819.3-2525, and 4U 1543-47) via comprehensive binary evolution simulations combined with parametric supernova modeling. It derives lower limits on common-envelope efficiency under three variants of the standard energy formalism (α_0.5U ≳ 6.7, α_U ≳ 4.2, α_H ≳ 1.7), reports that no solutions exist for efficiencies below unity even with enthalpy contributions, concludes that additional energy sources or formalism revisions are required, and finds that 4U 1543-47 formation demands natal kicks ≳ 50 km/s.

Significance. If the reconstructions hold, the work supplies concrete, observationally anchored lower bounds on CE efficiency in massive binaries, a dominant uncertainty in compact-object binary formation channels. The quantitative thresholds and the kick requirement for one system offer falsifiable inputs for population synthesis and could sharpen predictions for gravitational-wave sources.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of the manuscript, accurate summary of our results, and recommendation to accept. No major comments were raised requiring detailed responses.

Circularity Check

0 steps flagged

No circularity: constraints derived from matching external observations via standard simulations

full rationale

The paper performs binary evolution simulations across grids of initial conditions and CE efficiency parameters (α_0.5U, α_U, α_H) within the standard energy formalism, then identifies the minimum values that permit the final states to reproduce the observed properties (masses, periods, etc.) of the three specific BHXBs. This is a direct parameter constraint against independent external benchmarks rather than a self-referential loop. No quoted step reduces a claimed result to its own inputs by construction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz or renaming is smuggled in. The isolated-evolution premise is explicitly scoped, and the lower bounds are falsifiable by the same observations used as targets.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 0 invented entities

Only the abstract is available, so the full set of free parameters in the binary evolution code (initial masses, orbital periods, mass-transfer efficiencies, supernova kick distributions, envelope binding energy prescriptions) cannot be exhaustively listed. The work relies on the standard common-envelope energy formalism with variants and assumes isolated binary channels.

free parameters (1)
  • Common envelope efficiency parameters (α_0.5U, α_U, α_H)
    Lower bounds are derived by requiring evolutionary tracks to reproduce the observed properties of the three BHXBs; these act as fitted thresholds rather than independently measured quantities.
axioms (3)
  • domain assumption Standard energy formalism governs common envelope ejection
    Invoked throughout to define the efficiency parameters and binding energy calculations.
  • domain assumption These BHXBs formed via isolated binary evolution
    Central to the reconstruction approach; alternative channels are not considered.
  • domain assumption Parametric supernova modeling accurately captures natal kicks
    Used to assess kick requirements for 4U 1543-47.

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