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Issue
A&A
Volume 711, July 2026
Article Number L4
Number of page(s) 4
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/202659949
Published online 03 July 2026

© The Authors 2026

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model. This email address is being protected from spambots. You need JavaScript enabled to view it. to support open access publication.

1. Introduction

The bi-stability (BS) jump1 is a theoretically predicted, rapid change in radiatively driven wind properties around Teff ≃ 21–25 kK, associated with a transition from a fast, relatively tenuous wind to a slower, denser outflow. Vink et al. (1999, 2000) showed that the BS jump is fundamentally a temperature-driven ionisation effect, caused by the recombination of the dominant line driver iron from Fe IV to Fe III. Thus, it is no longer believed to be intrinsically tied to proximity to the Eddington limit, as originally suggested (Pauldrach & Puls 1990).

The mass-loss rates of OB supergiants are a key uncertainty in massive-star evolution, influencing envelope stripping, the formation of Wolf-Rayet stars, and the masses of black holes. Understanding whether the BS jump operates in nature is important well beyond the details of OB-star wind theory. It is central to interpretations of S Doradus variability in luminous blue variables (LBVs; Grassitelli et al. 2021) and supports the suggestion that LBVs could be direct supernova progenitors (Kotak & Vink 2006; Trundle et al. 2008). It has also been invoked to explain the formation of disks around Be and B[e] stars and aspherical winds (Lamers & Pauldrach 1991; Pelupessy et al. 2000; Curé et al. 2005). Yet, despite more than two decades of effort, empirical evidence of a clear BS jump signature in samples of OB supergiants remains elusive (Vink et al. 2000; Trundle & Lennon 2005; Crowther et al. 2006; Markova & Puls 2008).

In particular, Verhamme et al. (2024) reported a continuous decrease in Ṁ towards lower Teff. In contrast, most theoretical approaches predict a reversal in Ṁ across the Fe IV/Fe III transition. These include both global Monte Carlo (Vink et al. 1999) and work-ratio based CMFGEN (Petrov et al. 2016) modelling procedures, as well as more locally consistent approaches from Monte Carlo calculations (Vink 2018), METUJE models (Krtička et al. 2021), and hydrodynamically consistent PoWR models that utilise CMF radiative transfer (Sabhahit et al. 2026; Bernini-Peron et al. 2026). In contrast, the FASTWIND-based results of Björklund et al. (2023) display a more continuous behaviour without a reversal across the transition.

The goal of this Letter is to assess the robustness of BS jump predictions in hydrodynamically consistent PoWR models at low Γe. We also aim to clarify why most theoretical predictions and empirical mass-loss constraints appear to be in disagreement. The current theoretical status is that most models predict a BS jump, while some approaches predict a smoother behaviour without a clear reversal. Figure 1 of Verhamme et al. (2024) is particularly instructive in this respect. When the effective temperature decreases within the O-star regime, all approaches predict a decline in Ṁ, which Vink et al. (1999) attributed to a growing mismatch between the radiative flux distribution and the line opacity. However, once the temperature crosses the threshold where Fe III driving takes over from Fe IV, the predicted mass-loss behaviour is reversed in the majority of models.

This discrepancy is sometimes attributed to the proximity of LBVs to the Eddington limit, but this interpretation is not supported by the original Monte Carlo results, which show the BS jump over a wide range in Γe, and dynamical Monte Carlo models indicated that the relative strength of the BS jump increased towards lower Eddington parameters (Vink 2018). Finally, it is essential to distinguish between the BS jump in individual objects, where stellar parameters remain approximately constant while Teff changes, and population-based tests using samples of stars, where additional systematic differences may enter.

1.1. Origin of the bi-stability concept.

The BS jump was first uncovered in wind models of the LBV P Cygni by Pauldrach & Puls (1990) and its observational phenomenology was summarised by Lamers et al. (1995), who identified a change in terminal velocities and inferred wind densities around spectral type B1. In the earliest theoretical interpretations, the BS jump was linked to the optical depth of the Lyman continuum in objects close to the Eddington limit, motivating the idea that a change in the optical depth of the Lyman continuum would be responsible for the observed wind behaviour. Using Monte Carlo radiative transfer, Vink et al. (1999, 2000) revised this picture and demonstrated that the BS jump is present over a wide range of stellar parameters, including models far from the Eddington limit. The BS jump was shown to arise primarily from a temperature-dependent change in the flux-weighted line opacity, associated with the recombination of iron from Fe IV to Fe III when Teff drops below ∼21–25 kK2. In this framework, the Eddington parameter may modulate the onset and amplitude of the effect, but the physical origin is an ionisation-driven redistribution of line driving, rather than a sudden switch in Lyman continuum optical depth.

2. PoWR hydrodynamically consistent models

It is useful to distinguish between the physics of wind launching and the differential opacity effect responsible for the BS jump. Hydrodynamically consistent wind calculations can in some cases struggle to initiate a stationary outflow because of a decrease in the radiative acceleration in the wind launching region, also known as the ‘source-function dip’ (Gräfener & Hamann 2003). While such behaviour may reflect real physical difficulties in 1D stationary models, observations clearly demonstrate that O-type stars ubiquitously possess strong stellar winds. This suggests that nature finds ways to overcome the launching difficulty, potentially through multi-dimensional effects such as turbulent pressure or time-dependent structure. Once a wind solution is present, however, the Fe IV/Fe III ionisation transition produces a differential change in the line driving, leading to the characteristic mass-loss and velocity changes associated with the BS jump.

Sabhahit et al. (2026) investigated the dependence of mass-loss rates on the Eddington parameter, Γe, using hydrodynamically consistent PoWR model atmospheres. In addition to kinks in the Ṁ–Γe relation, the study revealed the presence of two distinct BS jumps. Interestingly, the bi-stable behaviour was found to be more prevalent at lower Γe than at higher Γe. The presence of the BS jump at Γe ≃ 0.4 has raised the question of whether BS would remain robust at even lower Γe.

To test this assumption, we extended the Sabhahit et al. (2026) analysis to Γe ≃ 0.2 by adopting a model with M = 40 M⊙ and log L/L⊙ = 5.5. We refer to Sabhahit et al. (2026) for details of the PoWR setup and modelling assumptions. In brief, wind clumping is incorporated using the micro-clumping approach. The clumping transitions from a smooth wind at the base (Dcl = 1) to a clumping factor of Dcl = 10 in the outer wind, with the onset of clumping at an optical depth of τcl = 0.1. The assumed metallicity is Z = 0.02, noting that while more recent solar compositions provide lower overall metallicities, the Fe abundance that sets the mass-loss BS jump should not be affected by this choice. Throughout this Letter, we distinguish between the inner boundary temperature, T★ (defined at τRoss = 20), and the effective temperature, Teff (defined at τRoss = 2/3), which is typically ∼1–2 kK lower with respect to the models considered here.

The mass-loss results in Fig. 1 show the expected jump, covering more than an order of magnitude, when a critical temperature is crossed. Here, this occurs at an inner boundary temperature of T★ ≃ 25 kK. This jump coincides with a dramatic increase in the contribution of Fe III to the line driving (Fig. 2). The same behaviour was previously found using Monte Carlo computations (Vink et al. 1999) and in CMFGEN models (Petrov et al. 2016).

Thumbnail: Fig. 1. Refer to the following caption and surrounding text. Fig. 1.

Ṁ versus T★, where T★ is the inner boundary effective temperature at Rosseland continuum optical depth τRoss = 20. Model parameters: log L/L⊙ = 5.5, M = 40 M⊙ (Γe ≃ 0.2), X = 0.7, Z = 0.02.

Thumbnail: Fig. 2. Refer to the following caption and surrounding text. Fig. 2.

Radiative acceleration contributions normalised to gravity and expressed as Eddington parameters from relevant Fe wind-driving ions at the critical point, expressed as function of T★ for the same model as in Fig. 1. These data illustrate the rise to Fe III dominance across the BS regime.

Figure 3 shows the corresponding drop in terminal wind velocity, in line with the observational constraints by Lamers et al. (1995) and Crowther et al. (2006) and the dynamically consistent Monte Carlo models of Vink (2018).

Thumbnail: Fig. 3. Refer to the following caption and surrounding text. Fig. 3.

Terminal wind velocity (v∞) versus T★ for the same model given in Fig. 1.

Thumbnail: Fig. 4. Refer to the following caption and surrounding text. Fig. 4.

Ṁ versus T★ for comparison models computed with a lower adopted turbulent velocity in the hydrodynamic equation (vturb = 21 km s−1). The two sequences have log L/L⊙ = 5.5 and different stellar masses, M = 30 M⊙ (Γe = 0.28) and M = 35 M⊙ (Γe = 0.24), corresponding to different Γe. Both sequences show a BS jump, with the lower-Γe model exhibiting a larger jump.

The mass-loss predictions of Sabhahit et al. (2026) have recently been adopted as input for spectral synthesis modelling of very massive stars by Sabhahit et al. (2025). In that work, a relatively high turbulent velocity3 was used in the hydrodynamic equation (vturb = 70 km s−1), motivated by recent multi-dimensional simulations for O-type stars (Moens et al. 2025). However, the mass-loss jump at the BS temperature is also present in the recent PoWR modelling study by Bernini-Peron et al. (2026), performed using lower assumed turbulent velocities in the hydrodynamic equation than the models in Sabhahit et al. (2026). That study also reported the same characteristic BS jumps, although those models were calculated for a somewhat higher Γe range.

For this reason, we performed additional sequences with more a moderate value of vturb = 21 km s−1. The results are shown in Fig. 4 for models with M = 30 M⊙ and M = 35 M⊙, corresponding to different Γe values at fixed luminosity. Both sequences show a clear BS jump. In fact, the model with lower Γe (in red) exhibits the larger jump, demonstrating that the jump strength does not scale monotonically with Γe. This further supports the interpretation that the BS jump is primarily a temperature-driven ionisation effect, rather than a direct consequence of Eddington limit proximity.

We conclude that while multi-dimensional effects of turbulence require substantially more rigorous investigation, current PoWR models across a range of turbulent-pressure assumptions and Γe values indicate that the BS jump is not restricted to high-Γe objects (e.g. LBVs and hypergiants). Instead, the mass-loss jump remains present down to relatively low Γe ∼ 0.2 values, well into the canonical B-supergiant regime. While proximity to the Eddington limit or the inclusion of a turbulent-pressure term can facilitate wind launching by reducing the effective gravity, the physical trigger of the BS jump remains the temperature-dependent Fe IV/Fe III ionisation balance.

3. Why empirical modelling does not reveal the predicted BS jump

The persistent absence of a clear BS jump signature in empirical mass-loss determinations for samples of OB supergiants has remained a major puzzle for more than 25 years (Vink et al. 2000). We do not attempt to resolve this discrepancy here; instead, we outline several independent considerations that may contribute to the tension between theoretical predictions and empirical analyses. The BS jump appears in the majority of independent modelling approaches, including global Monte Carlo calculations, CMFGEN models, and hydrodynamically consistent PoWR calculations. While the details of wind launching and the treatment of line driving differ between methodologies, the presence of the Fe IV/Fe III opacity transition is common to these models.

3.1. Considering whether the empirical mass-loss determinations are reliable

Even if the BS jump is physically real, empirical modelling may not yet be sufficiently sophisticated to recover it. Mass-loss determinations depend strongly on the assumed clumping factors and clumping prescriptions (Petrov et al. 2014; Driessen et al. 2019). In addition, empirical analyses often adopt different velocity laws on either side of the jump, with β values switching from β ∼ 1 to β ∼ 3, while most wind-driving calculations are 1D and do not self-consistently incorporate this change. Multi-dimensional effects, including latitudinal temperature dependence resulting from rotation, could also play a role (Gagnier et al. 2019; Hastings et al. 2023).

Systematic uncertainties are likely to be substantial. Indeed, for individual objects, different atmosphere codes and modelling strategies often produce mass-loss rates that differ by up to an order of magnitude (Alkousa et al. 2026). Differences in temperature definitions and reference radii (e.g. T★ versus Tτ = 2/3) could further complicate direct comparisons between theoretical and empirical temperature scales. As a result, a theoretically predicted change in mass-loss rate occurring over a relatively narrow temperature interval could be mapped onto a different or shifted range in empirical studies.

3.2. Mixed population effects and like-for-like tests

A fundamentally different issue is that the cool-side B supergiants might not, in fact, be the direct descendants of the hot-side O stars. As discussed by Vink et al. (2010), the cool-side objects may represent a distinct evolutionary population, potentially involving mergers (Menon et al. 2024). In particular, Vink et al. (2010) discussed two possible interpretations of the observed v sin i–Teff cliff: BS braking, or two distinct evolutionary populations.

Recent works indicate systematic differences across the B1 regime, including (i) a drop in the number of objects on the cool side in comparison to the hot side (de Burgos et al. 2024) and (ii) indications of a lower binary incidence on the cool side (Britavskiy et al. 2025; Patrick et al. 2025), consistent with an increasing role for post-interaction products and mergers (Menon et al. 2024). This would increasingly favour the second interpretation for the bulk of the observed v sin i versus Teff feature (Lennon et al. 2026). This does not imply that BS braking cannot occur in nature, nor that the issue of the terminal age main sequence (TAMS), especially at higher luminosities, is now resolved (Vink & Oudmaijer 2025). However, it does imply that population-based comparisons are unlikely to be like-for-like, which would undermine their ability to either prove or disprove BS jump physics directly.

For instance, if a substantial fraction of objects on the cool side of the jump are case B merger products, they could be under-luminous for their specific mass (Justham et al. 2014). Such differences in L/M (and hence Γe) would be expected to affect the wind properties and inferred mass-loss rates relative to the predominantly single-star population on the hot side of the feature.

3.3. Luminosity scaling and the interpretation of trends

Finally, some of the claimed observational trends could be driven by secondary parameters. For example, the continuous decrease in Ṁ with decreasing Teff reported by Verhamme et al. (2024) is based on a small number of objects at low Teff, predominantly at very low luminosities. When empirical mass-loss rates are scaled using luminosity-independent diagnostics such as the transformed mass-loss rate, the trend is partially (Bernini-Peron et al. 2024) or even fully reversed (Alkousa et al. 2026).

More generally, empirical constraints on the cool side of the BS jump remain sparse at higher luminosities. As a result, current samples may not yet provide a decisive test of whether a BS jump operates in the canonical B-supergiant regime at fixed L. Ultimately, the cleanest empirical test remains a controlled experiment using individual objects that undergo temperature excursions at approximately fixed stellar parameters, such as LBVs (Vink & de Koter 2002; Groh et al. 2011).

4. Discussion and conclusions

The main result of this note is that hydrodynamically consistent PoWR models predict a robust BS jump at T★ ≃ 25 kK even at relatively low Eddington parameters (Γe ≃ 0.2), confirming that the BS jump is not restricted to the high-Γ LBV regime. Instead, the jump is consistently associated with the temperature-driven recombination of iron from Fe IV to Fe III, in agreement with earlier Monte Carlo predictions (Vink et al. 1999, 2000) and CMFGEN calculations (Petrov et al. 2016). The persistence of this behaviour across independent CMF-based and hydrodynamically consistent approaches strengthens the case that the Fe IV/Fe III BS mechanism is a generic feature of line-driven winds.

At the same time, population-based empirical studies of OB supergiants have not revealed the predicted BS jump signature in mass-loss rates overall. We stress that such empirical tests may be fundamentally limited if the B supergiants on the cool side of the nominal BS jump do not represent the direct evolutionary continuation of the hot-side O-star population, as discussed in the two-population scenario of Vink et al. (2010). In fact, growing evidence points to systematic differences across the B1 regime, including indications of a lower binary incidence on the cool side (Britavskiy et al. 2025; Patrick et al. 2025), consistent with an increasing role for post-interaction products and mergers. In this scenario, the absence of a clear BS jump signature in heterogeneous samples cannot be regarded as a decisive falsification of the Fe IV/Fe III BS mechanism. Differences between current comoving-frame implementations remain to be understood and require dedicated benchmarking efforts. Future progress will likely require (i) targeted code-comparison studies, (ii) improved empirical wind modelling, in terms of clumping physics and wind hydrodynamics, and (iii) controlled observational tests using individual objects that undergo temperature excursions at approximately fixed stellar parameters, such as LBVs.

Acknowledgments

We thank the anonymous referee for constructive suggestions that helped strengthen the Letter. JSV and GNS are supported by the STFC grant ST/Y001338/1. AACS is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in the form of an Emmy Noether Research Group – Project-ID 445674056 (SA4064/1-1, PI Sander). AACS further acknowledges support by the Federal Ministry of Research, Technology and Space (BMFTR) and the Baden-Württemberg Ministry of Science as part of the Excellence Strategy of the German Federal and State Governments. This project was co-funded by the European Union (Project 101183150 – OCEANS).

References

  1. Abbott, D. C., & Lucy, L. B. 1985, ApJ, 288, 679 [NASA ADS] [CrossRef] [Google Scholar]
  2. Alkousa, T., Crowther, P. A., Bestenlehner, J. M., et al. 2026, A&A, 707, C1 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  3. Bernini-Peron, M., Sander, A. A. C., Ramachandran, V., et al. 2024, A&A, 692, A89 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  4. Bernini-Peron, M., Sander, A. A. C., Sabhahit, G. N., et al. 2026, A&A, 708, A206 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  5. Björklund, R., Sundqvist, J. O., Singh, S. M., Puls, J., & Najarro, F. 2023, A&A, 676, A109 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  6. Britavskiy, N., Mahy, L., Lennon, D. J., et al. 2025, A&A, 698, A40 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  7. Crowther, P. A., Lennon, D. J., & Walborn, N. R. 2006, A&A, 446, 279 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  8. Curé, M., Rial, D. F., & Cidale, L. 2005, A&A, 437, 929 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  9. de Burgos, A., Simón-Díaz, S., Urbaneja, M. A., & Puls, J. 2024, A&A, 687, A228 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  10. Driessen, F. A., Sundqvist, J. O., & Kee, N. D. 2019, A&A, 631, A172 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  11. Gagnier, D., Rieutord, M., Charbonnel, C., Putigny, B., & Espinosa Lara, F. 2019, A&A, 625, A88 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  12. Gräfener, G., & Hamann, W.-R. 2003, IAU Symp., 212, 190 [Google Scholar]
  13. Grassitelli, L., Langer, N., Mackey, J., et al. 2021, A&A, 647, A99 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  14. Groh, J. H., Hillier, D. J., & Damineli, A. 2011, ApJ, 736, 46 [CrossRef] [Google Scholar]
  15. Hastings, B., Langer, N., & Puls, J. 2023, A&A, 672, A60 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  16. Justham, S., Podsiadlowski, P., & Vink, J. S. 2014, ApJ, 796, 121 [NASA ADS] [CrossRef] [Google Scholar]
  17. Kotak, R., & Vink, J. S. 2006, A&A, 460, L5 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  18. Krtička, J., Kubát, J., & Krtičková, I. 2021, A&A, 647, A28 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  19. Lamers, H. J. G., & Pauldrach, A. W. A. 1991, A&A, 244, L5 [NASA ADS] [Google Scholar]
  20. Lamers, H. J. G. L. M., Snow, T. P., & Lindholm, D. M. 1995, ApJ, 455, 269 [Google Scholar]
  21. Lennon, D. J., Berlanas, S. R., Herrero, A., et al. 2026, A&A, 707, A204 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  22. Markova, N., & Puls, J. 2008, A&A, 478, 823 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  23. Menon, A., Ercolino, A., Urbaneja, M. A., et al. 2024, ApJ, 963, L42 [NASA ADS] [CrossRef] [Google Scholar]
  24. Moens, N., Debnath, D., Verhamme, O., et al. 2025, A&A, 704, A121 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  25. Müller, P. E., & Vink, J. S. 2008, A&A, 492, 493 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  26. Patrick, L. R., Lennon, D. J., Najarro, F., et al. 2025, A&A, 698, A39 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  27. Pauldrach, A. W. A., & Puls, J. 1990, A&A, 237, 409 [NASA ADS] [Google Scholar]
  28. Pelupessy, I., Lamers, H. J. G. L. M., & Vink, J. S. 2000, A&A, 359, 695 [NASA ADS] [Google Scholar]
  29. Petrov, B., Vink, J. S., & Gräfener, G. 2014, A&A, 565, A62 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  30. Petrov, B., Vink, J. S., & Gräfener, G. 2016, MNRAS, 458, 1999 [NASA ADS] [CrossRef] [Google Scholar]
  31. Sabhahit, G. N., Vink, J. S., Sander, A. A. C., et al. 2025, A&A, 696, A200 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  32. Sabhahit, G. N., Vink, J. S., & Sander, A. A. C. 2026, A&A, 706, A97 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  33. Trundle, C., & Lennon, D. J. 2005, A&A, 434, 677 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  34. Trundle, C., Kotak, R., Vink, J. S., & Meikle, W. P. S. 2008, A&A, 483, L47 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  35. Verhamme, O., Sundqvist, J., de Koter, A., et al. 2024, A&A, 692, A91 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  36. Vink, J. S. 2018, A&A, 619, A54 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  37. Vink, J. S., & de Koter, A. 2002, A&A, 393, 543 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  38. Vink, J. S., & Oudmaijer, R. D. 2025, Galaxies, 13, 19 [Google Scholar]
  39. Vink, J. S., de Koter, A., & Lamers, H. J. G. L. M. 1999, A&A, 350, 181 [Google Scholar]
  40. Vink, J. S., de Koter, A., & Lamers, H. J. G. L. M. 2000, A&A, 362, 295 [Google Scholar]
  41. Vink, J. S., Brott, I., Gräfener, G., et al. 2010, A&A, 512, L7 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
1

There is also a second BS jump at an effective temperature of roughly 10 kK, but this is not the focus of this Letter.

2

Using the global Abbott & Lucy (1985) MC method, Vink et al. (1999) found the mass-loss BS jump at 25 kK, while dynamically consistent modelling using the Müller & Vink (2008) Lambert W formalism, Vink (2018) found it closer 21 kK.

3

This turbulent velocity should not be confused with the microturbulence adopted in formal spectral synthesis.

All Figures

Thumbnail: Fig. 1. Refer to the following caption and surrounding text. Fig. 1.

Ṁ versus T★, where T★ is the inner boundary effective temperature at Rosseland continuum optical depth τRoss = 20. Model parameters: log L/L⊙ = 5.5, M = 40 M⊙ (Γe ≃ 0.2), X = 0.7, Z = 0.02.
In the text
Thumbnail: Fig. 2. Refer to the following caption and surrounding text. Fig. 2.

Radiative acceleration contributions normalised to gravity and expressed as Eddington parameters from relevant Fe wind-driving ions at the critical point, expressed as function of T★ for the same model as in Fig. 1. These data illustrate the rise to Fe III dominance across the BS regime.
In the text
Thumbnail: Fig. 3. Refer to the following caption and surrounding text. Fig. 3.

Terminal wind velocity (v∞) versus T★ for the same model given in Fig. 1.
In the text
Thumbnail: Fig. 4. Refer to the following caption and surrounding text. Fig. 4.

Ṁ versus T★ for comparison models computed with a lower adopted turbulent velocity in the hydrodynamic equation (vturb = 21 km s−1). The two sequences have log L/L⊙ = 5.5 and different stellar masses, M = 30 M⊙ (Γe = 0.28) and M = 35 M⊙ (Γe = 0.24), corresponding to different Γe. Both sequences show a BS jump, with the lower-Γe model exhibiting a larger jump.
In the text

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