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Minimum and maximum mass-luminosity relations for stripped stars

T0 review · 2 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Partially stripped stars can outshine pure-helium stars of the same mass by up to a factor of several, because a thin hydrogen-burning shell — not the helium core — dominates the energy output; the paper turns this into new mass-luminosity

desk verdict Worth taking seriously: the partially stripped MLRs fill a real gap and the non-monotonic luminosity behavior is credible, but the 'maximum' relation is only a maximum over a one-parameter linear-profile family, and the step-profile caveat is under-tested. read the letter →

arxiv 2508.14161 v1 pith:JOKQSO6U submitted 2025-08-19 astro-ph.SR astro-ph.HE

Gautham N. Sabhahit , Jorick S. Vink , Andreas A. C. Sander , Varsha Ramachandran This is my paper · ORCID
classification astro-ph.SRastro-ph.HE
keywords strippedstarsmass-luminosityrelationpartialstrippingheliumhydrogenshellburningEddingtonparameterstellarwindsWolf-Rayet
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

This paper asks how brightly a stripped star can shine for its mass after losing part or all of its hydrogen envelope, and answers with a result that reverses the usual expectation. Using synthetic stellar-structure models in which the leftover hydrogen is described by a single gradient slope, the authors find that luminosity rises with hydrogen content, peaks for a partially stripped configuration, and then falls toward the pure-helium value — so the most luminous configuration of a given mass is not the fully stripped one, but an intermediate one, brighter by a factor of two up to three or four. The cause is structural: the thin hydrogen-burning shell dominates the total luminosity budget even though the helium core holds most of the mass. The paper converts this into fitted minimum, maximum, and pure-helium mass-luminosity relations, and shows that the higher luminosities push these stars toward their Eddington limit, sharply raising predicted wind mass loss. That matters because partially stripped stars have recently been confirmed observationally, while the standard relations used to weigh them cover only the two extremes.

What carries the argument

The central object is the synthetic structure model: a MESA model built from a prescribed composition rather than evolved, with a pure-He core, an H-depleted envelope, and one H/He transition slope s = dX/dQ (Q a normalized mass coordinate; s = 0 fully homogeneous, s = ∞ pure He), relaxed to hydrostatic and thermal balance with burning and mixing switched off. These models expose the load-bearing mechanism: in a typical partially stripped star the H-burning shell contributes about three-quarters of the luminosity, the He core only about one-quarter. The practical machinery is fit relation Eq. (2) — the Gräfener et al. (2011) functional form plus an exponential XH term for the pure-He limit —

What would settle it

A partially or fully stripped star with a dynamically determined mass (from binary orbital motion) whose measured luminosity, for its measured surface hydrogen fraction, lies above the fitted maximum-luminosity curve by more than the ~0.03 dex fitting error — or below the minimum homogeneous curve — would refute the mass-luminosity relations. A softer check: measuring the wind of a star near the predicted maximum luminosity (e.g., a 10 solar-mass, XH = 0.1 object at log L/L_sun ≈ 5.48), where the models predict log Mdot ≈ -5.85 and v_inf ≈ 330 km/s; finding a fast (greater than 1000 km/s), wea

Watch

Extended reading notes

Core claim

For fixed total mass, stripped-star luminosity is non-monotonic in the hydrogen-profile slope s = dX/dQ: it rises steeply as a hydrogen-burning shell develops, peaks at an intermediate slope — the partially stripped configuration — then falls toward the pure-helium limit as opacity rises and mean molecular weight drops. The peak can exceed the pure-helium luminosity by a factor of roughly two, up to 3–4, overturning the homology intuition that the highest mean-molecular-weight configuration is the most luminous. The paper packages this into fit formulae for minimum, maximum, and pure-helium luminosities (and inverse masses), and shows with hydrodynamically consistent wind models that the Edd

Load-bearing premise

The load-bearing premise is that one linear hydrogen gradient — the slope s = dX/dQ — captures the range of H/He profiles that real stripping leaves behind; if semiconvective steps make actual profiles deviate strongly from linear, the location and height of the luminosity maximum, and the fits built on it, could shift.

Editorial extensions

If this is right

  • For a given luminosity and surface hydrogen fraction, a partially stripped star can be only about 60 percent as massive as a pure-helium star, so luminosity-based mass estimates for these objects need revision.
  • The maximum-luminosity curves bracket the measured masses and luminosities of the observed Magellanic Cloud stripped stars; the two lowest-mass objects are consistent with shallow slopes s ≈ 2–2.6, pointing to early core-He burning or Hertzsprung-gap binary stripping rather than wind stripping of an evolved supergiant.
  • At maximum luminosity, predicted mass-loss rates rise by about 1.5 dex and terminal velocities fall by about 1 dex relative to pure-He cases; over the few times 10^5 yr lifetime of the phase this can remove the entire residual envelope, turning a partially stripped star into a fully stripped one and potentially changing the supernova type (IIb vs. Ibc).
  • The wind models produce a double-horned He II 4686 Å emission profile in an otherwise cool spectrum, a signature that need not imply a disk or a black-hole companion.
  • For stars whose spectroscopically measured mass matches the pure-He value despite high surface hydrogen (2dFS 2553, Sk−71◦ 35), two different internal slopes are possible, so the relations define ranges of plausible internal structure rather than a unique answer.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the central claim holds, the most over-luminous stripped stars should be found at surface hydrogen fractions around 0.1–0.3, the regime where the luminosity excess peaks; the current observed sample, with XH ≈ 0.3–0.7, sits on the descending branch, so targeted searches there would give the cleanest test.
  • Eclipsing-binary or asteroseismic masses for a handful of partially stripped stars could break the degeneracy between shallow-slope (early stripping) and steep-slope (late stripping) interpretations that the two-way relations currently leave open.
  • The same synthetic-slope construction could be extended to re-expanding post-He-burning structures with both He and H shells — explicitly outside this grid — which would probably push the minimum mass for a given luminosity even lower and affect the interpretation of objects like 2dFS 163.
  • If the stronger winds are real, the mass lost during the partially stripped phase should leave an abundance fingerprint (e.g., altered N/C and He/H) in subsequent Wolf-Rayet and stripped-envelope supernova progenitors, giving an independent check on the predicted 0.1–0.5 solar-mass envelope removal.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This paper revisits mass-luminosity relations (MLRs) for stripped stars by constructing a large grid of MESA synthetic structure models (5910 models) that represent partially stripped stars as a pure-He core plus an H-depleted envelope with a linear H/He gradient of slope s = dX/dQ. The grid varies total mass, surface H abundance XH, slope s, and metallicity (Z = 0.008 and 0.004), with explicit convergence to thermal and hydrostatic balance (0.1% luminosity mismatch). The central result is that, for fixed mass and XH, luminosity is non-monotonic in s: it rises from the chemically homogeneous limit (s = 0), reaches a maximum at intermediate s, and then declines to the pure-He limit (s = ∞). The maximum can exceed the pure-He luminosity by a factor of 2–4, because the H-burning shell contributes disproportionately to the total luminosity. The authors provide fit formulae for minimum, maximum, and pure-He luminosities and their inverses, and demonstrate the impact of the higher luminosities on winds with PoWRhd hydrodynamic atmosphere models. They apply the relations to four observed partially stripped stars and discuss implications for their evolutionary channels and masses.

Significance. If the central claim holds, the paper fills a genuine gap: existing MLRs cover either chemically homogeneous or fully stripped pure-He stars, neither of which captures the partially stripped configurations that binary evolution and recent observations indicate are common. The predicted over-luminosity of partially stripped stars directly affects inferred masses, Eddington parameters, wind mass loss, and supernova progenitor interpretations. The paper's strengths include the large and systematically constructed model grid, the explicit thermal-balance convergence criterion, the dedicated evolution grid used to motivate the slope range, quantitative CNO-abundance tests (≤0.02 dex), and the public Python script/online calculator for the MLR fits. The comparison with observed partially stripped stars is a useful sanity check, and the wind models illustrate a potentially drastic luminosity dependence of mass loss. The work is not circular: the luminosity behavior is a numerical output, and the fit coefficients are presented as fits to the grid.

major comments (2)
  1. [Sect. 2.4 and Sect. 3.3] The maximum MLR (Eq. 2) is the envelope over the one-parameter family of linear H gradients. The authors assert in Sect. 2.4 that step-like H profiles from semiconvective/convective regions have only minimal effect because 'more H-rich material in the steps tends to reduce the luminosity,' so real structures fall between the predicted minimum and maximum. This assertion is not tested quantitatively. Since the central claim — that the maximum luminosity for a given mass and XH is captured by the linear-family maximum — is load-bearing for the inverse mass estimates in Sect. 3.4 and Table 2, I ask for a direct test: take representative H profiles from the evolution grid (especially those with large step-like features), construct MESA structure models with those exact profiles using the same relax_composition approach, and compare the resulting luminosities with the Lmin/Lmax curves of Eq.
  2. [Sect. 3.2 / Fig. 5] For high XH, the luminosity maximum occurs at effective temperatures below 10 kK (dashed lines in Fig. 5), which is cooler than the observed partially stripped stars used for comparison in Sect. 5. The authors discuss this and choose to rely mainly on mass and luminosity, which is reasonable, but the practical utility of the maximum MLR for hot, partially stripped stars is then less direct than the abstract suggests. I would like the text to state more explicitly over which temperature range the maximum relation is intended to apply, and whether the cool maximum structures are expected to be realized in nature given the inflation uncertainties.
minor comments (5)
  1. [Sect. 2.3] Minor typo: 'Mtot values ranges' should be 'Mtot values range'.
  2. [Sect. 3.3 / Table C.1] F10 is fixed to 0.005 rather than fitted; this should be noted in the main text near Eq. (2), as it may otherwise be confused with a free coefficient.
  3. [Fig. 5 and Appendix B] The abscissa uses e^{-1/s} to map s = 0 to 1 and s = ∞ to 0. This is useful, but the dual axis labels (e^{-1/s} and s) could be clarified in the caption, since the non-expert reader may wonder about the mapping.
  4. [Sect. 4] The PoWRhd wind models are only described by reference to Sabhahit et al. (2025); a sentence summarizing the inner boundary conditions or the mass-loss normalization would improve self-containedness.
  5. [Sect. 2.4] The statement that 'small and large step-like features can develop' would benefit from a figure or quantitative description of typical step amplitudes in the evolution grid, especially because the paper argues these steps do not affect the MLR extremes.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the maximum-luminosity result is a computed MESA grid output, and the MLR fits are explicit fits to that grid, not fitted inputs renamed as predictions.

full rationale

The central derivation chain is self-contained: the paper builds synthetic MESA structure models from fixed inputs (Mtot, Z, XH, slope s) and reads out the relaxed surface luminosity (Sect. 2.2). The non-monotonic L(s) behavior and the location of Lmax in Fig. 5 are numerical outputs of the structure calculation, not quantities imposed by the input parameterization. The MLR formulae in Eq. 2 are explicitly fits to the grid (Sect. 3.3, Table C.1), and the observed stars from Götberg et al. 2023 and Ramachandran et al. 2023, 2024 are overplotted after the fits are made, so they are not used to set the fit coefficients. The evolution grid in Sect. 2.4 is used only to motivate the plausible range of s (~1-30); the paper even extends the synthetic grid to s<1 for low XH to find maxima outside that range, so the maximum is not an artifact of a pre-chosen input interval. The self-citations (Sabhahit & Vink 2025 for inflation; Sabhahit et al. 2025 for PoWRhd model setup) concern secondary caveats and wind-model details, not the mass-luminosity derivation. The acknowledged limitation about step-like H profiles in Sect. 2.4 is a coverage/robustness concern, not a circular reduction of the prediction to its inputs.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new particles, forces, or conserved quantities. Its results rest on standard MESA physics, a one-parameter synthetic profile family, and fitted coefficients. The key physical output, H-shell-dominated over-luminosity, emerges from the models rather than being imposed.

free parameters (4)
  • MLR fit coefficients F1-F10 (Eq. 2) and s_max fit coefficients (Eq. D.1) = Tables C.1 and D.1 for Z=0.008 and Z=0.004
    Least-squares coefficients fitted to the MESA grid; F10 is fixed by hand to 0.005 to capture the nonlinearity below XH approximately 0.01 (Sect. 3.3).
  • H-profile slope s = dX/dQ (grid dimension) = s from 1 to 30 for 0<s<infinity; s=0 and infinity extremes; s in [0.75,0.9] added for low XH models
    The chemical profile input is parameterized by this single slope; the maximum luminosity occurs at intermediate s, so the choice of profile family directly shapes the central result.
  • Mixing length parameter alpha_MLT = 1.5
    Fixed MLT parameter, standard in stellar models; not varied in this work but affects the structure and luminosity.
  • Primordial helium Yprim and enrichment DeltaY/DeltaZ = Yprim = 0.24, DeltaY/DeltaZ = 2
    Fixed composition law from Audouze (1987) and Pols et al. (1998); determines initial X, Y, Z and the metal scaling.
assumptions (4)
  • domain assumption MESA structure models relaxed to hydrostatic and thermal equilibrium represent the luminosity of a real partially stripped star at a given composition profile
    The paper switches off nuclear burning and mixing (dxdt_nuc_factor=0, mix_factor=0) and requires luminosity stratification to match nuclear luminosity within 0.1% (Sect. 2.2).
  • ad hoc to paper The H/He composition of partially stripped stars is adequately represented by a single linear slope s = dX/dQ from surface XH to zero at the He core edge
    Sect. 2.2-2.3 construct the grid with this one-parameter profile family; step-like features from semiconvective mixing are argued to be minor (Sect. 2.4).
  • domain assumption The slope range s approximately 1-30 from the dedicated evolution grid brackets slopes of real partially stripped stars
    Sect. 2.4 fits slopes in evolutionary models with varied overshooting, semiconvection, rotation, and metallicity; the range is used to bound the synthetic grid.
  • domain assumption OPAL Type 2 opacities, OPAL-based EOS, and the 8-isotope basic.net network are sufficient for luminosity calculations
    Sect. 2.1 lists these standard MESA inputs without a dedicated convergence study beyond CNO abundance tests in Appendix A.

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Pith. "Pith review of Minimum and maximum mass-luminosity relations for stripped stars." pith.science (2026). https://pith.science/paper/JOKQSO6U

@misc{pith2026250814161,
  author       = {Pith},
  title        = {Pith review of: Minimum and maximum mass-luminosity relations for stripped stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JOKQSO6U}},
  note         = {Machine review of arXiv:2508.14161}
}
abstract

Envelope stripping, whether through single-star wind mass loss or binary mass transfer, is a key evolutionary pathway for the formation of classical Wolf-Rayet stars and lower-mass stripped helium (He) stars. However, to study the evolution of these objects into black holes, neutron stars, and stripped-envelope supernovae, we need appropriate input models for the core-He burning phase without relying on the uncertain evolution into this evolved phase. Reliable mass-luminosity relations (MLRs) for He stars are needed for stellar wind and evolution studies, but the MLRs currently in literature are either for fully-stripped or chemically homogeneous stars, neither of which reflect the important and recently also observationally confirmed stage of partial stripping. We alleviate this drawback by computing sets of MESA synthetic structure models with partially-stripped chemical profiles, consisting of a pure-He core and a hydrogen (H)-depleted envelope with an H/He chemical gradient left behind from the receding convective core during the main sequence. As the H slope increases from 0 (full chemical homogeneity) to $\infty$ (pure-He stars) in our synthetic models, we find the luminosity to initially increase before eventually decreasing. The maximum luminosity for a given mass is reached for an intermediate H-profile slope corresponding to a partially-stripped structure, exceeding even the values documented for pure-He stars, primarily due to the H shell disproportionately dominating the total luminosity budget. We also provide convenient mass-luminosity fit relations to predict the minimum, maximum, and pure-He luminosities for a given mass -- and vice versa -- while accounting for structures achievable through partial stripping. We also explore the impact of the higher luminosity on the wind properties of partially-stripped configurations using hydrodynamically consistent atmosphere models.

Figures

Figures reproduced from arXiv: 2508.14161 by the authors.

Figure 1
Figure 1. Chemical abundance profile of two synthetic models showcasing different H/He slopes. The mass fractions of hydrogen (X), helium (Y), and metals (Z) are shown in red, black and blue respectively. The top subplot has a H-profile slope of s = 2, while the bottom subplot has a higher slope of s = 5, with all other inputs fixed to the values shown in the title. The two extreme slope values of s = 0 and s = ∞ are also mar… view at source ↗
Figure 2
Figure 2. Evolution of H-profile slope s = dX/dQ as a function of effective temperature. The evolutionary model grid is built by varying the initial mass, convective overshooting, semiconvective mixing, rotation and initial metallicity (see text for the ranges spanned by these parameters). The sub-panels are divided based on the input overshooting and initial mass ranges. The tracks are colour-coded based on the input semicon… view at source ↗
Figure 3
Figure 3. Actual luminosity stratification compared to nuclear luminos￾ity inside a synthetic partially-stripped structure model in thermal bal￾ance. The specific nuclear energy generation rate, ϵnuc, in erg/g/s is also shown. This is the same model as in the top sub-plot of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Variation of surface luminosity (black) as a function of XH for different values of slope s for Z = 0.008. The parameter Mtot is fixed to 5 M⊙. The individual contributions from the He core (blue) and H shell (red) are also shown. The green dot indicates the luminosity…
Figure 5
Figure 5. Figure 5: Variation of luminosity as a function of slope s for different values of XH for Z = 0.008. The parameter Mtot is fixed to 5 M⊙. The abscissa goes from a fully chemically homogeneous model (s = 0) to a pure-He model (s = ∞). The minimum and maximum luminosities for a gi…
Figure 6
Figure 6. Figure 6: Minimum luminosity for a given total mass and surface XH. Left: Minimum luminosity plotted against surface XH for total masses ranging from 1 M⊙ to 40 M⊙. Right: Minimum luminosity plotted against total mass for XH values ranging from 0 to 0.7. The plus signs indicate …
Figure 7
Figure 7. Figure 7: Maximum luminosity for a given total mass and surface XH. Left: Maximum luminosity plotted against surface XH for total masses ranging from 1 M⊙ to 18 M⊙. Right: Maximum luminosity plotted against total mass for XH values ranging from 0 to 0.7. The plus signs indicate …
Figure 8
Figure 8. Figure 8: Left: Radiative acceleration normalized to gravity as a function of radius for four PoWRhd models, showing the individual contributions from various elements (coloured) and electron scattering (gray) to the total radiative acceleration (red dashed). Right: Radiative ac…
Figure 10
Figure 10. Figure 10: Synthetic normalized spectrum resulting from the four hydro￾dynamical wind models. the mass-loss rate increased by 1.5 dex, while the terminal ve￾locity decreased by 1 dex. We can further notice drastic changes to the acceleration structure by comparing the individual…

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Galactic intermediate-mass stripped star with a Wolf-Rayet-like wind

    astro-ph.SR 2026-08 conditional novelty 7.0 of 10

    WR 2-1 is the first unambiguous intermediate-mass stripped star in the Milky Way: a 3-6 solar mass, 60 kK helium-rich companion in a 5.94-day binary with a rapidly rotating O-star.

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