Mass-loss predictions for O and B stars as a function of metallicity

3); Alex de Koter (2); Henny J.G.L.M. Lamers (1) ((1) Astronomical Institute; Jorick S. Vink (1; London; Medicine; Technology; The Netherlands (2) Astronomical Institute; The Netherlands (3) Imperial College of Science; UK)

REVIEW

Mass-loss predictions for O and B stars as a function of metallicity

Jorick S. Vink (1, 3), Alex de Koter (2), Henny J.G.L.M. Lamers (1) ((1) Astronomical Institute, Utrecht University, The Netherlands (2) Astronomical Institute, University of Amsterdam, The Netherlands (3) Imperial College of Science

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Technology, Medicine, London, UK)

Astrophysics · Submitted 29 Jan 2001 · 47 references

Pith's verdict: A solid, widely used mass-loss recipe, but its single Z^0.85 term is an average that hides real per-temperature spread in the B-supergiant regime.

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arXiv IDastro-ph/0101509 (version 1)

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Citation3), Alex de Koter (2), Henny J.G.L.M. Lamers (1) ((1) Astronomical Institute, Jorick S. Vink (1, London, Medicine, Technology, The Netherlands (2) Astronomical Institute, The Netherlands (3) Imperial College of Science, UK), University of Amsterdam, Utrecht University. "Mass-loss predictions for O and B stars as a function of metallicity." arXiv:astro-ph/0101509 (2001). https://pith.science/paper/3UN24HLJ

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The thing to know: this is the paper that replaced the old square-root metallicity scaling with Mdot ∝ Z^0.85, and it is the recipe most evolution codes have leaned on since. The grid is real work — 540 self-consistent Monte Carlo wind models from 1/100 to 10 Zsun, momentum balance solved rather than assumed, uncertainties quoted on every fit coefficient, and an external check against SMC O stars in Fig. 7. The bi-stability jump relations (Eqs. 14, 15, 23) tying jump temperature to wind density and metallicity are new and useful, and Table 5, which tells you how to convert an iron-derived abundance into the oxygen-derived one the recipe assumes, is the kind of practical detail that makes a recipe actually usable by other people. The public code is a real plus. Where it is soft: the 0.85 is calibrated at one place in the grid — Teff = 50,000 K, v∞/vesc = 2.0 (Fig. 5, Eqs. 18–20). Transfer to everything else rests on one sentence in Sect. 7 that at other temperatures the jumps 'on average cancelled out', giving m = 0.85 ± 0.10. You can test that against their own Table 3 and it does not quite hold: at Γe = 0.434, v∞/vesc = 1.3, the slope over 1/30–3 Zsun runs from roughly 0.68 at 20 kK to about 1.04 at 12.5 kK. Some of that spread is the 25,000 K jump sliding through temperature as Z changes, which is a fair excuse — but it also means the single 0.85 in Eq. 25, which covers exactly that B-supergiant range, can be off by ~0.2 dex, a factor of 1.6 at 1/30 Zsun. A per-temperature table of slopes would have settled it; the average is asserted, not shown. Second, minor: the LMC comparison in Sect. 9 adopts Z = 0.8 Zsun after the 0.28 Zsun version left a 0.65 dex offset. They are upfront about why, and the SMC test is the cleaner one, but it reads as a choice made after seeing the residuals. Neither point breaks the central scaling. The O-star regime is well supported and the SMC comparison is honest. But if you are using Eq. 25 at low Z for B supergiants, treat the exponent as uncertain at the 0.2 level, not 0.1. Who should read it: anyone putting winds into evolution or population synthesis. It deserves a serious referee — the grid and the jump relations are substantial, and the exponent-transfer question is exactly what referees should push on.

Referee report

Significance

If the result holds, this is a genuinely useful paper: it replaces the widely used square-root metallicity scaling with a steeper, empirically calibrated power law and supplies a ready-to-use recipe with quoted fit uncertainties for evolutionary calculations at non-solar Z. Several features deserve explicit credit. The wind solutions are self-consistent in the sense that momentum balance is solved rather than assumed, and the Monte Carlo statistics are monitored (Sect. 3). The fits in Eqs. (18)–(20) carry formal uncertainties, and the recipe constants in Eqs. (24)–(25) carry uncertainties on every coefficient. The predictions are falsifiable: the positions of the bi-stability jumps and the Z^0.69 scaling can be tested against independent data, and the paper does test against SMC O stars (Fig. 7), which is external data rather than a re-description of the model grid. The announced public routine materially increases the paper's value to the community. The main caveat is that the recipe is a parameterization of the authors' own model output, so its authority rests on the observational comparisons in Sect. 9 and on the demonstrated constancy of the exponent; both of those deserve more

Major objections (3)

[Sect. 7, Eqs. (21)–(22), Table 3] The claim that m = 0.85 is constant across the grid, and the single +0.85 log(Z/Z⊙) term in Eqs. (24)–(25), rest on fits at one point in the grid: Teff = 50,000 K with v∞/vesc = 2.0 (Fig. 5, Eqs. 18–20, giving 0.842, 0.851, 0.878). Transfer to all other temperatures is supported only by the sentence in Sect. 7 that at other Teff 'on average, these jumps cancelled out', yielding m = 0.85 ± 0.10. Table 3 already contains the data needed to test this, and per-temperature slopes over 1/30–3 Z⊙ at fixed v∞/vesc do not sit within ±0.10 of 0.85. For Γe = 0.434, v∞/vesc = 1.3, the slopes are approximately 0.74 at 22.5 kK, 0.66 at 20 kK, 0.96 at 15 kK, and 1.02 at 12.5 kK; for Γe = 0.206, v∞/vesc = 2.0, approximately 1.02 at 12.5 kK and 0.88 at 25 kK. The spread is roughly 0.66 to 1.02, wider than the quoted ±0.10, and the largest deviations fall in the B-supergiant regime that Eq. (25) covers with a single 0.85. At Z/Z⊙ = 1/30 a 0.2 error in the exponent is a factor of about two in Mdot, which matters for exactly the low-metallicity evolutionary applications the paper targets. I ask the authors to add a per-temperature (and per-v∞/vesc) table of fitted exponents, restate the uncertainty on m as the actual scatter across the grid rather than a nominal ±0.10, and state explicitly the Z and Teff range over which the single-exponent recipe is accurate to, say, 0.1 dex.
[Sect. 9, Fig. 7] The abstract's claim that the predictions are 'successful in explaining the observed mass-loss rates for Galactic and Small Magellanic Cloud O-type stars' is the paper's principal external validation, but the SMC test as presented has limited discriminating power and the manuscript does not quantify it. Fig. 7 is reported to show 0.55 dex (1σ) scatter. At Z = 0.1 Z⊙, the difference between the new m = 0.85 and the previously standard m = 0.5 is only about 0.35 dex, which is smaller than the quoted scatter. The mean offset between theory and observation is therefore the quantity that carries the test, and it is not reported for Fig. 7 (it is reported only as a scatter for the LMC in Fig. 6). I ask the authors to give the mean offset and its standard error for the SMC sample, and to state which values of m are excluded at, say, 1σ and 2σ by that sample. If the SMC data cannot distinguish m = 0.85 from m = 0.5, the abstract and Sect. 10 should say so, and the validation claim should be softened accordingly.
[Sect. 6 and Sect. 7] Sect. 6 and Table 5 establish that the ion dominating the line acceleration near the sonic point switches from Fe at Z/Z⊙ ≳ 1/10 to CNO at Z/Z⊙ ≲ 1/30. The constancy of a single exponent in total Z across that switch is therefore a nontrivial empirical outcome rather than something guaranteed by the physics, and the manuscript treats it as an average without testing it. A direct check is available within the existing grid: fit the exponent separately over the Fe-dominated (Z/Z⊙ ≥ 1/10) and CNO-dominated (Z/Z⊙ ≤ 1/30) sub-ranges and compare. If the two sub-range exponents agree within the errors, the constancy claim is substantially strengthened and the paper should say so explicitly; if they differ, the single-term recipe needs a caveat in Sect. 8. Either outcome is worth reporting, and the present text leaves the reader unable to tell which it is.

Minor objections (9)

[Table 1 and Sect. 4] Table 1 lists abundances only for Z/Z⊙ = 1/30 through 3, but the grid extends to 1/100 and 10. The text notes that Y was held at 0.42 for Z/Z⊙ = 10; please add the 1/100 and 10 rows to Table 1, or state the adopted X, Y, Z for those points in the caption.
[Eq. (23)] The coefficient of Γe is 3.2 ± 2.2, a fractional uncertainty of about 70 percent, and this term sets the jump temperature that decides whether Eq. (24) or Eq. (25) is used in the 22,500–27,500 K window. Please state the implied uncertainty in T_jump and hence in the branch choice for the three adopted Γe values.
[Eqs. (14) and (23)] Eq. (23) supersedes Eq. (14) once the Γe dependence is included, but the text does not say so. Please add a sentence clarifying that Eq. (14) is the Z-only special case and that Eq. (23) is the form to be used in the recipe of Sect. 8.
[Table 4 and Sect. 5.1] The text states that there is 'no clear trend with metallicity' in the jump size, but Table 4 shows Δlog Mdot = 0.43 at Z/Z⊙ = 10 against 0.68–0.76 at the other metallicities. That is a decline at the highest Z and is consistent with the line-saturation argument in Sect. 2; please note it rather than describing the sizes as trendless.
[Sect. 5.2, Eqs. (16) and (17)] Eqs. (16) and (17) are given without uncertainties, whereas Eqs. (14), (15), and (23) all carry them. Please add uncertainties, or state explicitly that the additional jumps are too sparsely sampled for a formal error estimate.
[Sect. 9, Fig. 6] The improved LMC agreement in the lower panel of Fig. 6 rests on adopting Z_LMC = 0.8 Z⊙ from a single star, SK-67 o166 in Haser et al. (1998), in place of the standard nebular value 0.28 Z⊙. The manuscript is transparent about this, but the reader should be told that the LMC comparison is degenerate between the assumed Z and the predicted scaling, and that the 0.28 Z⊙ case is the conventional one. A sentence to that effect in Sect. 9 would prevent the lower panel from being read as an independent confirmation.
[Fig. 6 caption] The caption reads 'the Puls et al. (1996) Hα rates and de de Koter rates'; 'de de' is a typographical duplication.
[Sect. 8 and references] The text cites 'Achmad & Lamers 1997', but the reference list entry is 'Achmad L., Lamers H.J.G.L.M., Pasquini L., 1997'. Please make the in-text citation match the three-author reference.
[Fig. 1] The figure has seventeen panels and the text refers to individual panels by letter (e.g. panel (f), panel (o)). Please confirm that the panel labels are legible at print size, since the argument about the low-Z 35,000 K jump depends on the reader locating a specific panel.

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The paper

The paper claims

Mass loss from massive O and B stars follows a single power law in metal abundance over roughly 1/30 to 3 times solar metallicity.

The reading

The paper asks how strongly the winds of massive O and B stars depend on how many heavy elements the star contains. Using a Monte Carlo radiative-transfer wind model that follows photons through the outflow and counts multiple scatterings, the authors compute mass-loss rates across a grid of metallicities, temperatures, luminosities, and wind-speed ratios. They find that over roughly $1/30$ to $3$ times solar metallicity, mass loss follows a single power law in metallicity, with an exponent near $0.85$ when terminal wind speed is held fixed; folding in the cited $v_∞ ∝ Z^{0.13}$ gives $Ṁ ∝ Z^{0.69}$ for hot stars and $Ṁ ∝ Z^{0.64}$ for B supergiants. That matters because evolutionary calculations have often used a square-root dependence, which would underpredict how much mass low-metallicity massive stars retain. The authors package the result as an additive term in their earlier mass-loss recipe and check it against observed Galactic and Small Magellanic Cloud O stars.

What carries the argument

The load-bearing machinery is the Unified Monte Carlo wind model: a model atmosphere with non-LTE level populations supplies the density and temperature structure, then photon packets are followed through about 50-60 shells and more than $10^5$ spectral lines of H through Zn, with multiple scatterings counted, until the radiative momentum transferred matches the wind momentum. This avoids the core-halo split of classical line-driving treatments and lets the authors compute a self-consistent $Ṁ$ for each grid point. The metallicity dependence is extracted as the slope of $log Ṁ$ versus $log(Z/Z_⊙)$ at fixed temperature and wind-speed ratio, and the bi-stability jumps are handled by fitting the characteristic wind density at the jump and converting it to a jump temperature.

Extended reading notes

Core claim

The central claim is that, over $1/30 ≤ Z/Z_⊙ ≤ 3$, the mass-loss rate of massive stars obeys a single power law in metal abundance when the terminal wind speed is held fixed: $Ṁ ∝ Z^{0.85} v_∞^p$, with $p=-1.23$ for stars hotter than about $25{,}000$ K and $p=-1.60$ for B supergiants cooler than that. Feeding in the cited scaling $v_∞ ∝ Z^{0.13}$ turns this into an overall dependence $Ṁ ∝ Z^{0.69}$ for the hot stars and $Ṁ ∝ Z^{0.64}$ for the B supergiants. The exponent is reported as constant across that range, which is what licenses adding a single $+0.85 log(Z/Z_⊙)$ term to the earlier Vink et al. (2000) recipe on both sides of the $25{,}000$ K bi-stability jump. The authors also locate additional jumps caused by iron and carbon recombination and give formulae for their temperatures as functions of wind density.

Load-bearing premise

The load-bearing premise is that the exponent calibrated at $T_{eff}=50{,}000$ K and $v_∞/v_{esc}=2.0$, $m=0.85±0.10$, transfers unchanged to every other temperature and wind-speed ratio, with bi-stability jumps assumed to cancel on average; the paper itself notes that a pure power law may fail at the extremes and that the LMC abundance is uncertain, but the temperature-by-temperature constancy is asserted rather than tabulated.

Editorial extensions

If this is right

At $Z/Z_⊙=1/30$, the new exponent predicts an O-star mass-loss rate roughly a factor of ten below solar, where the old square-root rule would give only about a factor of five.
Evolutionary calculations that adopt the recipe should retain more envelope mass in low-metallicity massive stars and therefore end with different pre-supernova structures than calculations using $m=1/2$.
Population synthesis must include the bi-stability jumps at about $25{,}000$ K, $15{,}000$ K, and $35{,}000$ K; the recipe gives each jump temperature from the characteristic wind density.
At low metallicity, where CNO rather than iron dominates the line acceleration near the sonic point, oxygen-based abundance estimates are the appropriate input, and iron-based estimates need the conversion given in Table 5.
The publicly available routine lets other workers test the recipe against new low-metallicity observations.

Reading between the lines

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

A natural next test is to run the recipe inside a stellar-evolution code and see whether the lower low-$Z$ mass loss changes the predicted maximum black-hole mass or the stripped-envelope supernova fraction.
The $0.85$ exponent is close to the classical force-multiplier estimate $m=(1-α)/(α-δ) ≈ 0.8$; if multiple scattering mainly changes the normalization, the residual scatter in the fits should correlate with iron abundance rather than total $Z$.
The LMC comparison improves when one adopts $Z=0.8Z_⊙$ from a single O star; individual stellar abundances for the LMC and SMC samples would turn that post-hoc choice into a real test.
Because the carbon jump at $35{,}000$ K appears only at low $Z$ and low wind density, a targeted survey of hot, low-$Z$ dwarfs could look for the terminal-velocity change that the paper leaves open.

Original abstract

We have calculated a grid of massive star wind models and mass-loss rates for a wide range of metal abundances between 1/100 and 10 Z/Zsun. The calculation of this grid completes the Vink et al. (2000) mass-loss recipe with an additional parameter Z. We have found that the exponent of the power law dependence of mass loss vs. metallicity is constant in the range between 1/30 and 3 Z/Zsun. The mass-loss rate scales as Mdot \propto Z^0.85 Vinf^p with p = -1.23 for stars with Teff \ga 25000 K, and p = -1.60 for the B supergiants with Teff \la 25000 K. Taking also into account the metallicity dependence of Vinf, using the power law dependence Vinf \propto Z^0.13 from Leitherer et al. (1992), the overall result of mass loss as a function of metallicity can be represented by Mdot \propto Z^0.69 for stars with Teff \ga 25000 K, and Mdot \propto Z^0.64 for B supergiants with Teff \la 25000 K. Our mass-loss predictions are successful in explaining the observed mass-loss rates for Galactic and Small Magellanic Cloud O-type stars, as well as in predicting the observed Galactic bi-stability jump. Hence, we believe that our predictions are reliable and suggest that our mass-loss recipe be used in future evolutionary calculations of massive stars at different metal abundance. A computer routine to calculate mass loss is publicly available.

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What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.88 · mentions code or data availability 0.97.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We have calculated a grid of massive star wind models and mass-loss rates for a wide range of metal abundances between 1/100 and 10 Z/Zsun. The calculation of this grid completes the Vink et al. (2000) mass-loss recipe with an additional parameter Z. We have found that the exponent of the power law dependence of mass loss vs. metallicity is constant in the range between 1/30 and 3 Z/Zsun. The mass-loss rate scales as Mdot \propto Z^0.85 Vinf^p with p = -1.23 for stars with Teff \ga 25000 K, and p = -1.60 for the B supergiants with Teff \la 25000 K. Taking also into account the metallicity dependence of Vinf, using the power law dependence Vinf \propto Z^0.13 from Leitherer et al. (1992), the overall result of mass loss as a function of metallicity can be represented by Mdot \propto Z^0.69 for stars with Teff \ga 25000 K, and Mdot \propto Z^0.64 for B supergiants with Teff \la 25000 K. Our mass-loss predictions are successful in explaining the observed mass-loss rates for Galactic and Small Magellanic Cloud O-type stars, as well as in predicting the observed Galactic bi-stability jump. Hence, we believe that our predictions are reliable and suggest that our mass-loss recipe be used in future evolutionary calculations of massive stars at different metal abundance. A computer routine to calculate mass loss is publicly available.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We have calculated a grid of massive star wind models and mass-loss rates for a wide range of metal abundances between 1/100 and 10 Z/Zsun.	contribution 0.72	0.97	0.05	asserted 1.00
s1	The calculation of this grid completes the Vink et al. (2000) mass-loss recipe with an additional parameter Z.	contribution 0.76	0.74	0.08	asserted 1.00
s2	We have found that the exponent of the power law dependence of mass loss vs. metallicity is constant in the range between 1/30 and 3 Z/Zsun.	result 1.00	0.96	0.19	asserted 1.00
s3	The mass-loss rate scales as Mdot \propto Z^0.85 Vinf^p with p = -1.23 for stars with Teff \ga 25000 K, and p = -1.60 for the B supergiants with Teff \la 25000 K.	result 1.00	0.91	0.18	asserted 1.00
s4	Taking also into account the metallicity dependence of Vinf, using the power law dependence Vinf \propto Z^0.13 from Leitherer et al. (1992), the overall result of mass loss as a function of metallicity can be represented by Mdot \propto Z^0.69 for stars with Teff \ga 25000 K, and Mdot \propto Z^0.64 for B supergiants with Teff \la 25000 K.	result 1.00	0.66	0.37	asserted 0.99
s5	Our mass-loss predictions are successful in explaining the observed mass-loss rates for Galactic and Small Magellanic Cloud O-type stars, as well as in predicting the observed Galactic bi-stability jump.	result 0.84	0.83	0.32	asserted 1.00
s6	Hence, we believe that our predictions are reliable and suggest that our mass-loss recipe be used in future evolutionary calculations of massive stars at different metal abundance.	interpretation 0.52	0.35	0.55	hedged possibility 0.81
s7	A computer routine to calculate mass loss is publicly available.	contribution 0.81	0.57	0.03	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.66 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Continued. Series of M˙ (Z) calculations with Γe = 0.434 (log L/L⊙ = 6.0). The calculated mass loss as a function of Teff for seven metallicities in the range Z/Z⊙ = 1/100 - 10. The metal abundance is indicated in the legend at the upper part of each panel (k-q). The values for (v∞/vesc) are indicated in the legend of the last panel (q)

**Figure 2.** Characteristic density hρi at the bi-stability jump around 25 000 K as a function of Z. An explanation for the different symbols is given in the legend. The solid line indicates the best linear fit through the average jumps parameters for log hρi. 5.1. The bi-stability jump at Teff ≃ 25 000 K All panels show a bi-stability jump around Teff ≃ 25 000 K. Here, Fe iv recombines to Fe iii and as the latter ion is a more efficient line driver than the first, the acceleration in the lower part of the wind increases. This results in an upward jump in M˙ of about a factor of five and…

**Figure 3.** Characteristic density log hρi and Teff of the bistability jump around Teff = 25 000 K. An explanation for the different symbols is given in the legend. The solid line represents the best linear fit through the average jump parameters log hρi and Teff. (Z/Z⊙), a linear fit is plotted. This is the solid line in

**Figure 4.** The relative contribution to the line acceleration for models with (v∞/vesc) = 2.0, log L∗/L⊙ = 5.5 and M∗ = 40M⊙. The solid lines show the contribution of Fe lines. The dotted line is the contribution by C, N and O. The dashed line shows the contribution by H and He lines. (a) and (b) give the contribution for solar Z at resp. v = vsound and at v = 0.5v∞. (c) and (d) give the contribution for (Z/Z⊙) = 1/30 at resp. v = vsound and at v = 0.5v∞. our mass loss recipe will still yield the proper mass-loss rates. Only in those cases where the observed metallicity were determined from…

**Figure 5.** The M˙ (Z) dependence for three cases of Γe. In all three panels, the dashed lines indicate the best linear fit through the models at different Z. Note that at Γe = 0.130 the lowest Z model is not included in the fit, due to the presence of a bi-stability jump. All models have Teff = 50 000 K and constant (v∞/vesc) = 2.0. The values of Γe are indicated in the legends

**Figure 6.** Comparison between theoretical and observational M˙ for O stars in the LMC. The upper panel is for an adopted ZLMC = 0.28Z⊙ and the lower panel is for an adopted metallicity ZLMC = 0.8Z⊙. The Puls et al. (1996) Hα rates and de de Koter rates are indicated with different symbols. The dashed lines are one-to-one relations, tools for convenient comparison between observations and theory accurately known. What complicates a meaningful comparison is that there are differences in the observed stellar and nebular abundances. Additionally, there are abundance gradients present in these…

**Figure 7.** shows the comparison between observed massloss rates and our predictions for the sample of the SMC stars. The figure shows a reasonable agreement between predictions and observations. We admit that there is quite a large scatter (0.55 dex) for which there may be several reasons. The important point at this stage is that the comparison with the SMC data yields good average agreement and thus yields support to the reliability of our mass loss recipe at metallicities other than solar. For a test of our mass-loss recipe at extremely low Z, say Z/Z⊙ < 1/10, we will have to await new…

Figures reproduced from arXiv:astro-ph/0101509 by the authors.

References

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Forward citations

Cited by 47 Pith papers

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

Double Neutron Star Mergers and Fast Blue Optical Transients: A Circumbinary Disk Connection
astro-ph.HE 2026-11 accept novelty 7.0 of 10

Circumbinary disks from common envelope ejecta reduce double neutron star merger rates, produce luminous fast blue optical transients, and shift chirp mass distributions to higher values.
Core-Collapse Supernova Rates in the Dark Energy Survey
astro-ph.HE 2026-10 conditional novelty 7.0 of 10

Fitting 2,445 core-collapse supernovae from the Dark Energy Survey, the authors measure a volumetric explosion rate that rises as (1+z)^2.85 out to z=1.3, about 70 percent above star-formation-model predictions.
Quasar Impostors: Two Extremely UV-Bright ($M_{\rm UV}\approx-23.5$) Reionisation-Epoch Galaxies Powered by Very Massive Stars
astro-ph.GA 2026-08 conditional novelty 7.0 of 10

Two z~6.6-6.8 sources previously classified as faint quasars are reclassified as extremely UV-luminous galaxies whose spectra require very massive stars.
SPURS: Massive Stars, Dense Gas, and Ly$\alpha$ Escape in GN-z11 at $z = 10.6$
astro-ph.GA 2026-08 conditional novelty 7.0 of 10

GN-z11's rest-UV spectrum shows young massive stars with very massive star winds, dense gas, and a broad red Ly alpha wing that may help Ly alpha escape the largely neutral early universe.
A Helium-shell Burning Blue Horizontal Branch Star Produced from Common Envelope Evolution
astro-ph.SR 2026-08 conditional novelty 7.0 of 10

Feige 64 is a 0.35 solar mass helium-shell-burning BHB star in a 0.826-day orbit with a 1.26 solar mass white dwarf, best explained as a common-envelope remnant.

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Stellar winds of O-type stars traced by high ionization fine-structure emission lines with JWST/MIRI
astro-ph.SR 2026-06 unverdicted novelty 7.0 of 10

JWST/MIRI detects [Ne V] 14.3 micron emission from O-star winds in 5 of 22 observed stars, enabling wind speed and mass-loss rate estimates even in weak-wind regimes.
Collective Winds of Massive Star Clusters as the Dominant PeVatrons for Galactic Cosmic Rays
astro-ph.HE 2026-05 unverdicted novelty 7.0 of 10

A time-dependent model of stellar evolution and wind shocks shows collective winds of massive star clusters dominate the PeV knee and explain the common spectral break in protons and helium.
Modified Gravity and the Black Hole Mass Gap
gr-qc 2020-09 conditional novelty 7.0 of 10

Modified gravity that changes the effective gravitational constant lowers both edges of the black hole mass gap, and analysis of the first ten LIGO/Virgo events constrains the change to roughly ΔG/G_N ≈ 0.1 ± 0.1.
An Halpha survey of infrared bow-shocks around OB-type stars
astro-ph.SR 2026-07 conditional novelty 6.5 of 10

Fifteen plus one serendipitous clear H-alpha bow shocks are detected among 78 IR candidates; several are consistent with radiation-supported regimes while others match classical wind-supported shocks.
Asteroseismic forward modelling of 36 $\beta$ Cep pulsators and inferences on their internal differential rotation
astro-ph.SR 2026-07 conditional novelty 6.5 of 10

Forward modelling of 36 β Cep stars with second-order rotation effects shows internal rotation declining with age and common radial differential rotation, often non-monotonic, in 17 stars.
The formation and evolution of Wolf-Rayet stars with temperature-dependent winds
astro-ph.SR 2026-11 conditional novelty 6.0 of 10

Adding the temperature dependence of Wolf-Rayet wind mass loss to single and binary MESA models makes low-metallicity stars stall at 70 to 90 kK, matching the observed temperature clustering of SMC Wolf-Rayet stars.
The STARfall pathway: forging intermediate-mass black holes through stellar collisions in dense star clusters
astro-ph.GA 2026-11 conditional novelty 6.0 of 10

Semi-analytic simulations show that stellar collisions in ultradense star clusters can form very massive stars that collapse into intermediate-mass black holes of 1,000-10,000 solar masses.
Surface Nitrogen enrichment from the LMC to the Early Universe: the roles of rotation, overshooting and mass loss
astro-ph.SR 2026-11 accept novelty 6.0 of 10

Modest rotation, not extreme mixing, can explain why many massive stars in the LMC show surface nitrogen enrichment.
Beyond Mergers: the Role of Metallicity in Forming a Reservoir of Massive and Detached Binary Black Hole Systems
astro-ph.SR 2026-10 conditional novelty 6.0 of 10

At moderate metallicities, massive black holes in binaries are predominantly left in wide detached orbits rather than merging, creating a reservoir for dynamical hardening.
Shaping binary black hole merger efficiency with gravitational wave observations
astro-ph.HE 2026-09 conditional novelty 6.0 of 10

A hierarchical Bayesian fit to GWTC-5.0 constrains BBH merger efficiencies, favoring a suppression of the isolated-channel efficiency by O(10) and a dynamically-formed channel efficiency about 16 to 30 times larger th...
In-Situ Star Formation in a Thick Disk: A Model for Metal Enrichment of Mrk 573
astro-ph.HE 2026-09 conditional novelty 6.0 of 10

A Salpeter population of 10-30 solar mass stars forming in-situ in a thick accretion disk (H/r ~ 0.1) can explain the metal enrichment of Mrk 573, while a thin disk cannot.
N/O-enhanced chemical enrichment by massive stars: the interplay of optically-thick winds and rotation
astro-ph.GA 2026-09 conditional novelty 6.0 of 10

Rotating massive stars with optically-thick winds produce C/O-rich ejecta that drive a fast N/O-to-normal transition, reproducing the abundance patterns of three high-z WR galaxies.
Evidence for the emergence of stellar magnetic fields during rapid mass transfer
astro-ph.SR 2026-09 conditional novelty 6.0 of 10

Plaskett's Star is argued to be a post-mass-transfer binary with a 5.9 solar mass stripped donor and a 40.8 solar mass magnetic accretor, linking rapid mass transfer to the emergence of stellar magnetism.
RIGEL: Ultra-faint dwarf galaxy diversity shaped by inhomogeneous cosmic reionization
astro-ph.GA 2026-09 accept novelty 6.0 of 10

Simulations with realistic patchy reionization show that the diversity of ultra-faint dwarf galaxies is primarily controlled by the halo mass at the moment of reionization.
The Mass-Ratio Distribution of the Low-Mass Binary Black Hole Subpopulation: A Natural Outcome of Isolated Binary Evolution
astro-ph.HE 2026-09 conditional novelty 6.0 of 10

Detailed binary population synthesis shows isolated binary evolution naturally produces a two-component mass-ratio distribution consistent with the low-mass merging black hole subpopulation observed by gravitational w...
The ALMA carbon monoxide supernova (ACOS) survey II. Turbulent giant molecular clouds at the positions of core-collapse supernovae
astro-ph.GA 2026-08 conditional novelty 6.0 of 10

Core-collapse supernovae are found in molecular gas with median CO(2-1) velocity dispersion of about 9 km/s, versus 3.8 km/s for typical host-galaxy pixels.
The symphony of pulsations and binarity among massive stars using HERMES spectroscopy and TESS photometry
astro-ph.SR 2026-08 conditional novelty 6.0 of 10

An ensemble analysis of 873 O/B stars shows photometric variability in >93%, pulsations in ~82%, and evidence of binarity in at least 14%, including 30 newly discovered eclipsing binaries.
The progenitors and circumstellar environments of stripped-envelope interacting supernovae from BPASS
astro-ph.HE 2026-08 conditional novelty 6.0 of 10

Using BPASS, only binary progenitors whose mass loss forms a circum-binary disc reproduce the luminosities and rise times of stripped-envelope interacting supernovae.
Formation of rotating supergiants via stellar mergers in dense clusters: Implications for black hole natal spins
astro-ph.HE 2026-07 conditional novelty 6.0 of 10

Stellar mergers with mass ratio q≳0.3 in young clusters can produce blue-supergiant progenitors that leave black holes with dimensionless spins a≃0.5–0.8, reducing post-merger retention and hierarchical-merger rates.
A grid of fast-rotating, chemically-homogeneous, supernova and/or long-GRB progenitors
astro-ph.HE 2026-06 unverdicted novelty 6.0 of 10

Presents a grid of 113 fast-rotating, chemically-homogeneous massive star models at Z=0.001 reaching core collapse with high angular momentum for use as supernova and GRB progenitors.
A Kinematic Study of Wolf-Rayet Stars at the Galactic Center I: Binary Candidates and Constraints on the Binary Fraction
astro-ph.GA 2026-06 unverdicted novelty 6.0 of 10

30-year kinematic monitoring of 27 Galactic center Wolf-Rayet stars identifies five binary candidates and infers a binary fraction of 0.56 ± 0.18.
Massquerade: Impacts of Mass Ratio Reversals on Binary Black Hole Merger Rates and Mass Distributions
astro-ph.HE 2026-05 unverdicted novelty 6.0 of 10

Mass ratio reversals produce qualitatively different contributions to BBH merger rates and masses in COMPAS versus SEVN simulations, with core-growth dominating and most systems arising from massive low-metallicity pr...
Neutron star-companion interaction in core collapse supernovae. Population synthesis based on detailed binary evolution models
astro-ph.SR 2026-05 unverdicted novelty 6.0 of 10

Population synthesis from binary evolution models predicts periodic neutron star-companion interactions in more than half of surviving hydrogen-poor core-collapse supernovae, with periods peaking at 20-50 days and las...
GeV {\gamma}-ray emission in the low-mass star-forming region AFGL 490
astro-ph.HE 2026-05 unverdicted novelty 6.0 of 10

Discovery of extended GeV gamma-ray emission from AFGL 490, with the protostellar jet identified as the likely particle accelerator rather than stellar winds.
Photometric variability of blue supergiants: Constraints on stellar masses and evolutionary stages
astro-ph.SR 2026-10 conditional novelty 5.0 of 10

TESS photometry matched to radial nonadiabatic pulsation models yields first mass estimates for six blue supergiants and tentative evolutionary-stage assignments.
Wolf-Rayet formation through L/M-dependent superwinds
astro-ph.SR 2026-10 conditional novelty 5.0 of 10

An L/M-dependent red supergiant wind law drives runaway envelope stripping, allowing ~20 solar-mass stars to form Wolf-Rayet stars as single stars.
Probing the Mass--Redshift Dependence of Binary Black Holes and its Implications for $H_0$ with GWTC-5.0
astro-ph.CO 2026-09 conditional novelty 5.0 of 10

Copula-based population models of 235 GWTC-5.0 black hole mergers show no strong mass-redshift dependence and leave the Hubble constant estimate, about 74 km/s/Mpc with broad errors, unchanged within its uncertainty.
Can isolated binaries form unequal-mass binary black-hole mergers with a high-spin primary black hole?
astro-ph.SR 2026-09 accept novelty 5.0 of 10

Isolated binary evolution can produce unequal-mass binary black hole mergers with a high-spin primary black hole via two specific pathways, offering alternatives to hierarchical mergers.
Characterization of the variability of the blue supergiant HD 14134
astro-ph.SR 2026-08 conditional novelty 5.0 of 10

HD 14134 is a post-main-sequence blue supergiant with a 19.2-day g-mode pulsation and wind variability that may dominate its TESS brightness changes, questioning its alpha Cyg variable classification.
The effect of near-core mixing on rejuvenation and the asteroseismic properties of massive accretors
astro-ph.SR 2026-06 unverdicted novelty 5.0 of 10

1D models show convective boundary mixing dominates the asteroseismic imprint of accretion in massive stars, robust to semiconvection changes but drastically altered without it, with thermal relaxation as key.
Targeting black holes from metal-poor progenitors with next-generation gravitational-wave detectors
astro-ph.HE 2026-06 unverdicted novelty 5.0 of 10

Introduces a target redshift z_t to isolate metal-poor black hole progenitors and a statistical framework to test merger-rate variations against forecasts from Einstein Telescope and Cosmic Explorer.
Mergers via failed common envelope as a route towards intermediate-mass stripped stars
astro-ph.SR 2026-05 unverdicted novelty 5.0 of 10

Failed common envelope mergers yield 6-14 solar mass stripped stars consistent with long-lived core He-burning objects that appear single or in wide binaries from hierarchical triples.
Probing Heavy Axion-like Particles from Massive Stars with X-rays and Gamma Rays
hep-ph 2024-12 conditional novelty 5.0 of 10

Decay photons from heavy ALPs produced in Wolf-Rayet stars can be probed by INTEGRAL SPI down to gaγ ~ 4e-11 GeV^-1 for ma ~ 10-100 keV, modestly extending existing limits.
Merging binary black holes formed through chemically homogeneous evolution in short-period stellar binaries
astro-ph.HE 2015-12 conditional novelty 5.0 of 10

Chemically homogeneous evolution in tidally locked massive binaries yields a local binary black hole merger rate of about 10 Gpc^-3 yr^-1, peaking near 20 at z about 0.5, with typical total masses of 50 to 110 solar masses.
Detection of new Galactic Wolf-Rayet stars with SPHEREx
astro-ph.SR 2026-09 conditional novelty 4.0 of 10

SPHEREx spectrophotometry confirms 13 new Galactic Wolf-Rayet stars plus 3 probable Wolf-Rayet-type planetary nebula central stars from machine-learning Gaia XP candidates.
SN 2023rve: A Type II Supernova with No Nebular Oxygen
astro-ph.HE 2026-06 unverdicted novelty 4.0 of 10

SN 2023rve exhibits absent [O I] nebular lines with inferred 14-18 solar mass progenitor, 0.27e51 erg explosion energy, and 0.0064 solar mass nickel, possibly indicating partial fallback.
Evolution of Compact Stellar Systems in Ultralight Dark Matter Halos: Dependence on Stellar and Dark Matter Parameters
astro-ph.GA 2026-06 unverdicted novelty 4.0 of 10

Simulations find metal-richer compact stellar systems resist disruption better in ULDM halos, with tidal fields altering stability and heating strengthening at higher particle masses when system size is much smaller t...
Comparative Study of Two Luminous Red Novae I. Progenitor Modeling and Dust Formation
astro-ph.SR 2026-06 unverdicted novelty 4.0 of 10

Binary evolution modeling constrains donor masses of 14-23 solar masses for two luminous red novae and shows dust masses are 1-5 orders of magnitude below total ejected envelope masses.
Can current models predict the local black hole merger rate?
astro-ph.HE 2026-06 unverdicted novelty 3.0 of 10

Theoretical predictions for local BBH merger rates exceed observations by a factor >10 under conservative SFRD and metallicity assumptions, indicating need for revisions in stellar evolution.
The origins of massive black holes
astro-ph.GA 2021-10 accept novelty 3.0 of 10

No new result: the authors synthesize the proposed formation channels for massive black hole seeds and the electromagnetic and gravitational wave observations that could discriminate among them.
Population Synthesis of Gravitational Wave Sources
astro-ph.HE 2025-02 accept novelty 1.0 of 10

A review of population synthesis: the codes, the environments, and the predicted rates and features of gravitational wave sources, with an emphasis on breaking degeneracies.
The School on Gravity: from motion to commotion
gr-qc 2026-10 unverdicted

This review compiles pedagogical lectures on the formation, detection, and dynamics of compact object binaries, the effective-field-theory approach to the two-body problem, and the quantum properties of black holes.

How later papers used it

481 later papers cite it

Evidence: substantial. 460 of the citing papers share no author with it, and 259 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 863 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

16 later papers by other authors are listed below: 15 used its method or tool and 1 used its data or values. 2 more papers by the same authors are listed: 1 used its method or tool and 1 compared its own results with it.

Uses its method or tool 16 of 225 papers with this label · 1 by the same authors

Included stellar winds from both components following this paper's prescription.

The eclipsing binary systems with $\delta$ Scuti component -- II. AB Cas (2022) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper's prescription for the core hydrogen burning phase.

Massive black holes regulated by luminous blue variable mass loss and magnetic fields (2019) · 1.00 · paraphrased: the licence does not allow quoting
Wind driven mass loss follows the prescriptions of [ref] for stars with $>10^4K$ and surface hydrogen mass fraction $X_H>0.4$, [ref] for $>10^4K$ and surface $X_H<0.4$, and [ref] at all other times, with wind-scaling factors of 1.0.

The cosmic carbon footprint of massive stars stripped in binary systems (2021) · Pre-supernova evolution · 1.00
For the mass loss in our models, we adopt the so-called “Dutch" scheme, employing the Vink et al. [ref] prescription for hot phases and the de Jager, Nieuwenhuijzen, and van der Hucht [ref] prescription for cool phases.

The Effect of Mass Loss and Convective Overshooting on the Pre-Collapse Structure, Composition, and Neutrino Emission of Red Supergiants (2026) · Modeling Red Supergiants with · 1.00
Followed this paper for the winds.

Close Encounters of Wide Binaries Induced by the Galactic Tide: Implications for Stellar Mergers and Gravitational-Wave Sources (2024) · 1.00 · paraphrased: the licence does not allow quoting
Computed mass loss rates for hydrogen-rich models following this paper, using a metallicity scaling of (Z/Zsun)^0.85.

Related progenitor models for long-duration gamma ray bursts and Type Ic superluminous supernovae (2018) · 1.00 · paraphrased: the licence does not allow quoting
Employed a prescription combining the models of this paper for effective temperatures above 4000 K.

A Model for Eruptive Mass Loss in Massive Stars (2024) · 1.00 · paraphrased: the licence does not allow quoting
Evolved stars to black holes using a package that includes updated prescriptions for stellar winds and mass loss from this paper.

Reconstructing the Genealogy of LIGO-Virgo Black Holes (2024) · 1.00 · paraphrased: the licence does not allow quoting
Stellar winds are included using the algorithms from [ref] with an efficiency factor of 1.

The Stellar Merger Scenario for Black Holes in the Pair-instability Gap (2020) · setup · 1.00
For each progenitor star with zero-age main-sequence (ZAMS) mass $M_⋆$ at $t=2.2$ Myr, we apply metallicity-dependent wind mass loss using the [ref] prescription over the remaining main-sequence lifetime ($∼1 - 2$ Myr for $M_⋆≳250$), obtaining a pre-collapse mass $M_pre$.

Repopulating the pair-instability mass gap without sustained growth to massive IMBHs: the case of 47\,Tuc (2026) · Seed Models · 1.00
Adopted the Dutch wind model, which combines the models of this paper and another work.

Metallicity Ceiling in Quasars from Recycled Stellar Winds (2022) · 1.00 · paraphrased: the licence does not allow quoting
Both sets rely on the wind mass-loss recipe of [ref] .

A model of anisotropic winds from rotating stars for evolutionary calculations (2023) · Numerical method · 1.00
Adopted this paper's metallicity-dependent stellar wind prescriptions to determine the final stellar mass at core collapse.

Populating the upper black hole mass gap through stellar collisions in young star clusters (2020) · 1.00 · paraphrased: the licence does not allow quoting
Followed this paper's theoretical prescription for wind mass loss during hot phases with surface hydrogen mass fraction at least 0.4.

How much hydrogen is in Type Ib and IIb supernova progenitors? (2021) · 1.00 · paraphrased: the licence does not allow quoting
This configuration applies [ref] for thin and low-$Γ_e$ thick winds (see more in Section [ref]).

The Stellar Winds Atlas I: Current uncertainties in mass-loss rates (2026) · Wind Scheme Implementations · 1.00

By the same authors

Hot O stars ($T_eff>10$kK) with surface hydrogen mass fraction $X_s>0.4$ use the metallicity-dependent mass loss recipe from [ref] .

Superadiabaticity and the metallicity independence of the Humphreys-Davidson limit (2021) (same authors) · Mass loss · 1.00

Uses its data or values 1 of 27 papers with this label

Used equation (21) of this paper, which suggests the mass loss rate scales with metallicity as Z^0.85.

Effect of mass loss due to stellar winds on the formation of supermassive black hole seeds in dense nuclear star clusters (2021) · 0.80 · paraphrased: the licence does not allow quoting

Compares with it 1 of 30 papers with this label · 1 by the same authors

By the same authors

For example, in Fig. [ref], we notice that while both the [ref] rates and our hydrodynamical predictions agree at the Arches transition, the two prescriptions exhibit very different behaviour above and below the transition.

Hydrodynamical mass-loss rates for Very Massive Stars II. New theoretical mass-loss predictions at solar metallicity (Z = 0.02) (2026) (same authors) · Comparison to other recipes · 1.00

How the literature uses it

69 arXiv papers cite this in 155 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 69 sentences without a confident label

Contests it 6 papers

Again these comparisons and simple averages show quite clearly that the sudden increase in mass-loss rate predicted at the supposed bi-stability jump by the [ref] prescription is not present in these observational results.

X-Shooting ULLYSES: Massive Stars at low metallicity IX: Empirical constraints on mass-loss rates and clumping parameters for OB supergiants in the Large Magellanic Cloud · Is there a generic mass loss jump in the range $T_eff ∼15 - 35$ kK? · contest 0.91
All research groups come to the conclusion that the [ref] prescription should be used cautiously, as it may overestimate the mass loss by up to a factor of 10–100 for stars cooler than 25 kK, agreeing more closely with the trends predicted by [ref] .

X-Shooting ULLYSES: Massive stars at low metallicity XV. On the metallicity dependence of B-supergiant mass-loss rates · Introduction · contest 0.75
Consequently, population synthesis codes adopting [ref] , [ref] , or [ref] likely overestimate mass-loss rates in the optically thin winds regime, accelerating the depletion of hydrogen (H)-rich envelopes and leading to premature formation of WR stars.

The Stellar Winds Atlas I: Current uncertainties in mass-loss rates · Mass-loss rates · contest 0.85

Uses its method or tool 27 papers

* Optically thin winds: For $logg≥3.0$ we use [ref] , hereafter GM23, while for $logg<3.0$ we adopt [ref] , hereafter V01.

The Stellar Winds Atlas II: Black Hole Formation at Solar Metallicity · Free-Electron Scattering transition (FESc) Models · 0.99
The initial mass function is evolved through the single stellar evolution code $SSE$ by [ref] , with updated wind mass loss prescription [ref] , (pulsational) pair instability or (P)PISN recipe [ref] and supernova kick Maxwellian distribution (with $σ=265km/s$) from [ref] ; scaled by fallback mass for BHs [ref] .

Repopulating the pair-instability mass gap without sustained growth to massive IMBHs: the case of 47\,Tuc · Methods · 1.00
We parameterise the wind terminal speed as a temperature dependent multiple of the escape speed, [equation] The escape speed is [equation] To mimic the usual bi-stability behaviour we adopt a two-branch scaling [ref] , [equation] We take $η_hot=2.6$, $η_cool=1.3$, and $T_bist=2.1×10^4 K$.

Habitable Zones Around Massive Stars: From the Main Sequence to Supergiants · Stellar evolution tracks · 0.92

Uses its data or values 4 papers

The mass-loss prescription relevant for our work uses the mass-loss rate of [ref] during the main sequence phase, that of [ref] for the RSG phase, and those of [ref] and [ref] for the WR phase.

Multi-Dimensional MHD simulations of young Core-Collapse Supernova Remnants · Stellar model · 0.91
We adopt $f_DC = 0.6$ for $Z = 0.003$ and $f_DC = 0.45$ for $Z = 0.007$, reflecting the stronger wind mass loss at higher metallicity [ref] .

Repopulating the pair-instability mass gap without sustained growth to massive IMBHs: the case of 47\,Tuc · Seed Models · 0.94
Furthermore, [ref] found that the metallicity exponent ($α$) of the mass loss rate is constant in a wide range of metallicities $1/30 ≤Z/≤3$, with $= 0.019$ [ref] .

Stellar Black Holes and Compact Stellar Remnants · Mass loss through stellar winds · 0.92

Compares with it 10 papers

In the context of the present study, the main difference in the predictions of these schemes is that [ref] predict significantly higher mass-loss rates for stars below $T_eff ∼22-25$ kK than for hotter stars, whereas [ref] do not predict such a jump but instead a steady decrease of mass-loss rates with decreasing temperature.

X-Shooting ULLYSES: Massive Stars at low metallicity IX: Empirical constraints on mass-loss rates and clumping parameters for OB supergiants in the Large Magellanic Cloud · Is there a generic mass loss jump in the range $T_eff ∼15 - 35$ kK? · 0.93
We show that different but widely used models for extremely massive star wind rates ( [ref] versus [ref] ) result in final IMBH masses differing by a factor of $∼4$.

FROST-CLUSTERS -- III. Metallicity-dependent intermediate mass black hole formation by runaway collisions in dense star clusters · Summary and conclusions · 0.81
We show that the mass-loss rates from [ref] , despite representing the weaker optically thin wind regime, predict similar mass-loss rates to [ref] and [ref] at $logL ≳6.3$, and higher than [ref] for $logL ≲6.05$.

The Stellar Winds Atlas I: Current uncertainties in mass-loss rates · Mass-loss rates · 0.99

Cites it as support 1 paper

At the metallicities of interest for this channel, $Z ≲0.004$, the radiatively driven winds are strongly reduced as predicted by [ref] and empirically verified by [ref] .

Merging binary black holes formed through chemically homogeneous evolution in short-period stellar binaries · The role of stellar winds: mass loss and angular momentum loss · 0.97

Cites it as background 10 papers

Although these early results already hinted at the possibility of a corresponding increase in $Ṁ$, such an increase was quantified by [ref] .

X-Shooting ULLYSES: Massive Stars at low metallicity IX: Empirical constraints on mass-loss rates and clumping parameters for OB supergiants in the Large Magellanic Cloud · Introduction · 0.81
The most widely used prescription for stellar mass loss in the hot upper Hertzsprung–Russell diagram, and a benchmark, is the pioneering work by [ref] , which features a bi-stability jump.

X-Shooting ULLYSES: Massive stars at low metallicity XV. On the metallicity dependence of B-supergiant mass-loss rates · Introduction · 0.85
In particular, the second bi-stability jump occurring at T $∼$ 8800 K due to the recombination of Fe iii to Fe ii is the most relevant in the context of yellow hypergiants and post-RSG objects [ref] .

Spatial and spectral constraints on resolved mass-loss of the massive Post-RSG star IRAS 17163-3907 and its Fried Egg Nebula · Introduction · 0.82

Discussion

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