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arxiv: 2604.05406 · v2 · submitted 2026-04-07 · 🌌 astro-ph.SR

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Adiabatic Mass Loss In Binary Stars. VI. Massive Helium Binary Stars

Lifu Zhang , Hongwei Ge , Zhenwei Li , Hailiang Chen , Dengkai Jiang , Guoliang L\"u , Xiaofeng Wang , Xuefei Chen
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Zhanwen Han
Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:47 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords helium starsbinary mass transfercritical mass ratioWolf-Rayet binariesadiabatic mass lossstellar windsbinary evolutionhigh-mass X-ray binaries
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The pith

Adiabatic mass-loss models revise the critical mass ratios for unstable transfer in massive helium binaries.

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

This paper computes how naked helium stars from 10 to 80 solar masses respond to rapid mass loss while staying in equilibrium. It finds new ranges for the critical mass ratio that separates stable from dynamically unstable Roche-lobe overflow. When mass transfer is fully non-conservative, main-sequence helium stars become unstable at lower mass ratios than the commonly used value of 3, while Hertzsprung-gap helium stars stay stable to higher ratios than the usual value of 4. These updated criteria affect predictions for the evolution of Wolf-Rayet binaries and high-mass X-ray binaries with helium companions. The work supports more accurate binary population synthesis for objects like merging double black holes.

Core claim

We systematically calculate the adiabatic mass-loss model for naked helium stars with masses ranging from 10 to 80 solar masses to study the critical mass ratio of Wolf-Rayet binaries. Results of the critical mass ratio for conserved dynamically unstable mass transfer show that most of the no-wind helium stars on the main sequence have 0.7 < q_crit < 3.0 and on the Hertzsprung gap have 1.5 < q_crit < 27. Based on fully non-conserved mass transfer, the criteria for HeMS stars are 1.0 < q_crit < 2.8 and HeHG stars are 1.5 < q_crit < 5.0. Compared with the widely used criterion q_crit=3 (HeMS) and q_crit=4 (HeHG), our result becomes more unstable for the HeMS stars and more stable for the HeHG.

What carries the argument

The adiabatic mass-loss response of naked helium stars under Roche-lobe overflow, incorporating stellar wind prescriptions and isotropic re-emission, which sets the critical mass ratio q_crit separating stable and dynamically unstable mass transfer.

Load-bearing premise

The helium star remains in hydrostatic equilibrium during mass loss, with the transfer rate set solely by the Roche-lobe overflow condition and without thermal readjustment.

What would settle it

A comparison of the observed mass-ratio distribution or survival fraction of Wolf-Rayet binaries and high-mass X-ray binaries against the predicted instability thresholds from the 10-80 solar mass adiabatic models.

Figures

Figures reproduced from arXiv: 2604.05406 by Dengkai Jiang, Guoliang L\"u, Hailiang Chen, Hongwei Ge, Lifu Zhang, Xiaofeng Wang, Xuefei Chen, Zhanwen Han, Zhenwei Li.

Figure 1
Figure 1. Figure 1: Evolutionary track of a naked 60 M⊙ helium star with no wind. In this Paper, ’log’ represents the base-10 logarithm. The left panel shows the full evolutionary track from the beginning of HRD, and the right panel shows star age versus stellar radius after He-ZAMS. For the left panel, the black dashed line represents an 80 M⊙normal hydrogen envelope star evolving after the MS. The green line is the process … view at source ↗
Figure 2
Figure 2. Figure 2: Evolutionary track of naked helium stars on the HR diagram. The left panel shows the models without wind, and the right panel contains 0.8 times Nugis & Lamers wind. Both sequences are evolved from 10 − 80 M⊙ He-ZAMS stars. The color represents the changes in mass during stellar evolution. Due to the no-wind prescription on the left panel, the color is constant. The grey dashed lines in both panels are the… view at source ↗
Figure 3
Figure 3. Figure 3: MCO of helium star sequences. The x-axis is the helium star mass, and the y-axis is MCO for this specific model. Similar to [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The evolutionary track on the HR diagram (left) and the conserved critical mass ratio (right) for the selected models with different wind prescriptions. The grey dashed lines represent the models that reach He-TAMS. Both four evolution curves start from one 50 M⊙ He-ZAMS model (the square marker). With different wind schemes, massive helium stars evolve to different masses, as shown by the colors of the do… view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The radius evolution during the adiabatic mass loss of two massive helium stars. They share similar mass and radius but in different wind schemes. The left panel shows a no-wind model with 30 M⊙, which just evolves to the early HeHG stage. The right panel shows a model with the η = 0.8 wind scheme and an initial mass of 50 M⊙, which has evolved to the late HeHG stage. The black lines are the surface radius… view at source ↗
Figure 7
Figure 7. Figure 7: The results of qcrit for the conserved mass transfer prescription in the M − R parameter space. The left panel is for the no-wind scheme, and the right one is for the η = 0.8 scheme. The grey-dashed area on the right panel is the same space as the one to the left. The maximum field of the chosen helium star models sets the boundary for HeMS in the right panel. Due to the Wind-driven Decortication Effect, t… view at source ↗
Figure 8
Figure 8. Figure 8: The distribution of critical mass ratio on Mass-Radius in period-mass ratio parameter space. The panels are based on different treatments of angular momentum loss. The top panel is conserved mass transfer, and the bottom panel is the completely non-conserved mass transfer of isotropic re-emission angular momentum loss (β = 1). The colorbar represents the stellar mass. The horizontal lines are the elder cri… view at source ↗
Figure 9
Figure 9. Figure 9: The structure of M˙ th,crit for 10 M⊙, 17 M⊙, 25 M⊙ and 40 M⊙ helium stars with no wind. The horizontal dot lines are the mass loss rates of η = 1 Nugis & Lamers wind. The colors of the different lines correspond to a specific helium-star model on the HRD on the right. B. THE LOCAL THERMAL TIMESCALE PROFILES AND THE SIGNIFICANCE OF WIND DECORTICATION To show the significance of Wind-driven Decortication Ef… view at source ↗
Figure 10
Figure 10. Figure 10: The qcrit of specific stellar models and the RBF interpolate. The color represents the qcrit and the text has a similar meaning to [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
read the original abstract

The stability of binary mass transfer is a critical problem for binary evolution. We systematically calculate the adiabatic mass-loss model for naked helium stars with masses ranging from 10$M_{\odot}$ to 80$M_{\odot}$ to study the critical mass ratio ($q_\textrm{crit}$) of Wolf-Rayet binaries. We set up two prescriptions about Wolf-Rayet stellar wind and consider the isotropic re-emission effect during adiabatic mass loss. Results of the critical mass ratio for conserved dynamically unstable mass transfer show that most of the no-wind helium stars on the main sequence (HeMS) have $0.7<q_\textrm{crit}<3.0$ and on the Hertzsprung gap (HeHG) have $1.5<q_\textrm{crit}<27$. With the Wolf-Rayet star wind effect, the $q_\textrm{crit}$ gets lower on a certain evolutionary stage. With the isotropic re-emission effect, the $q_\textrm{crit}$ gets larger for early-evolutionary stage helium stars and lower for late-evolutionary stage helium stars. Based on fully non-conserved mass transfer, the criteria for HeMS stars are $1.0<q_\textrm{crit}<2.8$ and HeHG stars are $1.5<q_\textrm{crit}<5.0$. Compared with the widely used criterion $q_\textrm{crit}=3$ (HeMS) and $q_\textrm{crit}=4$ (HeHG), our result becomes more unstable for the HeMS stars and more stable for the HeHG stars. Our work could be applied to the binary mass transfer stage of massive helium binaries, such as Wolf-Rayet star binaries and high mass X-ray binaries with Wolf-Rayet star companions. It can be applied to the binary population synthesis studies for the formation of special objects, such as double black hole mergers.

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

1 major / 0 minor

Summary. The paper computes adiabatic mass-loss responses for naked helium stars (10-80 M_sun) across main-sequence (HeMS) and Hertzsprung-gap (HeHG) stages to derive critical mass ratios q_crit for dynamical instability under conserved and non-conserved mass transfer. Two Wolf-Rayet wind prescriptions and isotropic re-emission are included. Reported ranges include 0.7 < q_crit < 3.0 (HeMS) and 1.5 < q_crit < 27 (HeHG) for conserved no-wind cases, with winds lowering q_crit at certain stages and re-emission raising it early and lowering it late; for fully non-conserved transfer the ranges are 1.0 < q_crit < 2.8 (HeMS) and 1.5 < q_crit < 5.0 (HeHG), which the authors compare to the commonly adopted values of 3 and 4.

Significance. If the adiabatic results hold, the work supplies updated, mass- and stage-dependent q_crit criteria that can be directly inserted into binary population synthesis codes for Wolf-Rayet binaries and high-mass X-ray binaries. The systematic coverage of wind prescriptions and re-emission across a wide mass range, together with explicit numerical ranges rather than single-parameter fits, constitutes a concrete advance over the fixed q_crit=3/4 values currently in wide use.

major comments (1)
  1. [Model setup] Model setup (as described for the 10-80 M_sun helium-star grid): the central q_crit values rest on the assumption that the donor remains in strict hydrostatic equilibrium with mass-transfer rate fixed solely by the Roche-lobe condition and no thermal adjustment. For these massive stars, especially on the HeHG where the star is expanding, the Kelvin-Helmholtz timescale can become comparable to the RLOF timescale; the actual radius response would then lie between the pure adiabatic and thermal-equilibrium limits, shifting the mass ratio at which zeta_ad exceeds zeta_RL and therefore changing the reported boundaries 1.0 < q_crit < 2.8 (HeMS) and 1.5 < q_crit < 5.0 (HeHG).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of the significance of our work and for the constructive comment on the model assumptions. We address the major comment point by point below.

read point-by-point responses

  1. Referee: Model setup (as described for the 10-80 M_sun helium-star grid): the central q_crit values rest on the assumption that the donor remains in strict hydrostatic equilibrium with mass-transfer rate fixed solely by the Roche-lobe condition and no thermal adjustment. For these massive stars, especially on the HeHG where the star is expanding, the Kelvin-Helmholtz timescale can become comparable to the RLOF timescale; the actual radius response would then lie between the pure adiabatic and thermal-equilibrium limits, shifting the mass ratio at which zeta_ad exceeds zeta_RL and therefore changing the reported boundaries 1.0 < q_crit < 2.8 (HeMS) and 1.5 < q_crit < 5.0 (HeHG).

    Authors: We agree that the strict adiabatic assumption is an idealization and that the referee correctly notes the potential comparability of the Kelvin-Helmholtz and RLOF timescales for some HeHG models. Our calculations are deliberately adiabatic, following the established methodology of the preceding papers in this series, because the adiabatic response (zeta_ad) governs whether runaway mass transfer develops on the dynamical timescale before thermal relaxation can occur. When zeta_ad exceeds zeta_RL, the donor expands faster than the Roche lobe even in the most unstable limit; an intermediate thermal response would only make the system more stable. Thus our reported q_crit ranges mark the boundary for immediate dynamical instability. We will add a dedicated paragraph in the discussion section acknowledging this limitation, noting that real systems may exhibit responses between the adiabatic and thermal-equilibrium limits, and clarifying that the tabulated values are therefore conservative for population-synthesis applications. This constitutes a partial revision. revision: partial

Circularity Check

0 steps flagged

No circularity: q_crit ranges derived directly from numerical adiabatic response calculations

full rationale

The paper computes adiabatic mass-loss responses for 10-80 M_sun helium stars by solving the stellar structure equations under hydrostatic equilibrium and the Roche-lobe overflow condition, then identifies q_crit as the mass ratio where the adiabatic radius response zeta_ad exceeds the Roche-lobe zeta_RL. This is a forward numerical derivation from the model setup and does not reduce to any fitted parameter, self-defined quantity, or load-bearing self-citation; the resulting ranges (1.0 < q_crit < 2.8 for HeMS and 1.5 < q_crit < 5.0 for HeHG under fully non-conserved transfer) are outputs of the integration, not inputs. Prior papers in the series supply the general method but the specific massive-helium-star grids and wind/re-emission prescriptions are independent computations. No step renames a known result or imports uniqueness via self-citation.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the adiabatic approximation for the stellar radius response, two specific Wolf-Rayet wind prescriptions whose functional forms are not given in the abstract, and the assumption that mass leaves the system isotropically during non-conservative transfer. No new particles or forces are postulated.

free parameters (2)
  • Wolf-Rayet wind prescription parameters
    Two different wind recipes are adopted; their scaling constants and dependence on luminosity or mass are chosen from prior literature and not re-derived here.
  • Isotropic re-emission efficiency
    The fraction of transferred mass that is ejected isotropically is treated as a free modeling choice that alters q_crit differently at early and late evolutionary stages.
axioms (2)
  • domain assumption The helium star remains in hydrostatic equilibrium during rapid mass loss so that its radius change is governed by the adiabatic index.
    This is the defining assumption of the adiabatic mass-loss model used throughout the series.
  • domain assumption Mass transfer is either fully conservative or fully non-conservative with isotropic re-emission; no intermediate angular-momentum loss channels are modeled.
    The two limiting cases are used to bracket the critical mass ratios reported in the abstract.

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