Pith. sign in

REVIEW 4 major objections 7 minor 72 references

The Effect of Rotation on Triggering S Doradus Instabilities in Luminous Blue Variables

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Rotation makes luminous blue variables hit their modified Eddington limit at the equator first, triggering S Dor eruptions at higher effective temperatures and shaping disk-like outflows.

desk verdict First explicit rotating-star MEL trigger criterion with testable equator/pole predictions, but the numerical thresholds have a factor-of-two inconsistency that needs fixing. read the letter →

arxiv 2502.09504 v1 pith:V5ZYUFCZ submitted 2025-02-13 astro-ph.SR

Emily M. Levesque , Henny J. G. L. M. Lamers , Alex de Koter This is my paper · ORCID
classification astro-ph.SR
keywords luminousbluevariablesSDoradusvariationsmodifiedEddingtonlimitstellarrotationgravitydarkeningmasslosscircumstellarnebulaeinstability
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 argues that rotation is a trigger condition for S Doradus eruptions in luminous blue variables, not a side effect. Building on the modified Eddington limit, where radiation pressure leaves only ten percent of Newtonian gravity, the authors derive a rotation-dependent criterion for when the equator and the poles become unstable. Because rotation lowers the equatorial temperature and raises the maximum atmospheric opacity reached there, a faster rotator crosses the instability threshold at a higher effective temperature and at the equator before the poles. The result is that rotation broadens the observed S Dor instability strip and predicts dense equatorial disks or rings alongside high-velocity bipolar outflows, matching nebulae seen around stars like AG Car and HR Car.

What carries the argument

The load-bearing object is the rotationally modified Eddington criterion, Equation (24): $(L/M)_{\mathrm{crit,eq}} = 1.17\times10^4\,\Psi(\omega)/\kappa_{\max}(T_{\mathrm{eq}})$. It combines three pieces: the adopted instability threshold $\Gamma_{\mathrm{mod}}=0.9$ (effective gravity reduced to ten percent of Newtonian gravity), the von Zeipel gravity-darkening law that makes the equator cooler than the poles, and the opacity peak $\kappa_{\max}(T_{\mathrm{eff}})$, which rises toward roughly 12000 K so a cooler equator experiences stronger radiation pressure. The ratio $\Psi(\omega)$ encodes how much of the total luminosity is emitted from the polar caps of a distorted rotating star. Together these imply that the equator hits the instability first and that faster rotation shifts the trigger to higher effective temperatures.

What would settle it

A direct test is to gather a sample of post-main-sequence LBVs with measured $v\sin i$ and high-cadence S Dor light curves: the claim predicts that for matched $L/M$, faster rotators enter eruption at higher effective temperatures, and that equatorial disk-like nebulae appear preferentially around fast rotators. A cleaner single observation would be spectropolarimetry of an LBV beginning an S Dor eruption, since the mechanism predicts the equatorial wind turns on before the polar wind.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that the modified Eddington limit of a rotating post-main-sequence luminous blue variable is set by the equator rather than by the mean stellar surface. The instability criterion becomes $(L/M)_{\mathrm{crit,eq}} = 1.17\times10^4\,\Psi(\omega)/\kappa_{\max}(T_{\mathrm{eq}})$, where $\Psi(\omega)=L_{\mathrm{tot}}/L_{\mathrm{p}}$ measures how rotation redistributes luminosity toward the poles and $\kappa_{\max}(T_{\mathrm{eq}})$ is the maximum photospheric opacity at the cooler equatorial temperature. Since $\kappa_{\max}$ grows as the effective temperature falls, rotation makes the equatorial atmosphere reach $\Gamma_{\mathrm{mod}}=0.9$ at a higher effective temperature and at a lower $L/M$ than a non-rotator would need. In the numerical grid built from Geneva evolutionary tracks, most LBVs are unstable at both poles and equator, while lower-mass and slower-rotating cases are stable or equator-only; the models reproduce observed equatorial rings and bipolar nebulae.

Load-bearing premise

The quantitative trigger rests on the adopted threshold from Ulmer and Fitzpatrick: an atmosphere is unstable when radiation pressure reduces effective gravity to ten percent of Newtonian gravity; if the true threshold differs, the temperatures and $L/M$ values at which S Dor eruptions start shift, even though the equator-first ordering from rotation may survive.

Editorial extensions

If this is right

  • At fixed $L/M$, a faster rotating LBV reaches the modified Eddington limit at a higher effective temperature than a non-rotator, so rotation broadens the S Dor strip in the Hertzsprung-Russell diagram.
  • The equatorial instability is triggered before the polar one; at low $\omega$ the equator's instability spreads over the full surface, while at high $\omega$ it can remain equator-only and launch a disk or ring.
  • Most Galactic models with $M_i > 40\,M_\odot$ are unstable at both poles and equator even without rotation, whereas $32$ to $40\,M_\odot$ stars need rotation ($\omega \gtrsim 0.6$) to become unstable.
  • The predicted mass-loss geometry, with a dense slow equatorial wind and a faster polar wind, matches the bipolar nebulae of AG Car and HR Car and the equatorial disks inferred for R127 and SN 2009ip.
  • Lower-metallicity SMC models are more stable than Galactic ones because their post-main-sequence masses are higher and their opacities lower, implying that the incidence of LBV instability should depend on metallicity.

Reading between the lines

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

  • If the equator-first trigger holds, high-resolution spectropolarimetry of an LBV at the start of an S Dor eruption should catch the equatorial wind turning on before the polar wind, a signature this paper does not test directly.
  • The same rotation-modified Eddington logic should apply to other opacity-driven instabilities in massive stars, such as the Humphreys-Davidson limit, potentially shifting the predicted red supergiant upper luminosity boundary for rotating stars.
  • A testable extension is to compare $v\sin i$ measurements across a large LBV sample with nebular morphology: this mechanism predicts a positive correlation between rotation rate and the presence of equatorial disk or ring features.
  • The analysis assumes latitude-independent rotation, so differential rotation or magnetic coupling could change the quantitative thresholds; the equator-first ordering itself likely survives because it only requires $T_{\mathrm{eq}} < T_{\mathrm{p}}$.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 7 minor

Summary. The paper studies how stellar rotation modifies the Modified Eddington Limit (MEL) criterion that is believed to trigger S Doradus-type instabilities in Luminous Blue Variables (LBVs). Adopting the Ulmer & Fitzpatrick (1998) threshold that a non-rotating atmosphere becomes unstable when radiation pressure reduces the effective gravity to 10% of Newtonian gravity (Γ_mod = 0.9), the authors extend the criterion to rotating stars. They derive closed-form expressions for the critical L/M ratio at the equator (Eq. 24) and at the pole (Eq. 25), incorporating the von Zeipel gravity-darkening law, the centrifugal term, and the rotation-dependent surface and luminosity factors Ψ(ω). They apply these criteria to model LBVs built from Geneva evolutionary tracks at Z = 0.014 and Z = 0.002, computing instability flags at ω = 0, 0.3, 0.6, and 0.9 (Table 3), polar and equatorial temperatures and escape speeds, and wind speed ratios. The central claims are that rotation lowers the critical L/M and raises the triggering T_mean at fixed L/M, that the equator becomes unstable before the poles, that rotation broadens the S Dor strip, that most model LBVs are unstable even without rotation, and that the equator/pole asymmetry predicts equatorial disk or ring morphologies and faster polar outflows, which the authors compare with observations of AG Car, HR Car, R127, SN 2009ip, and HD 160529. The paper is explicit about its simplifying assumptions, which are listed in Section 7.

Significance. If the derived criterion is correct, the paper supplies a compact, falsifiable framework for the role of rotation in LBV variability: the equator-first instability ordering, the Ψ(ω)-dependent threshold, and the prediction that rotation broadens the S Dor strip all translate directly into observational programs (rotation-rate surveys, nebular imaging, metallicity-dependent LBV demographics). The analytic derivation is transparent, and the explicit power-law fits in Appendix A make the thresholds in Figures 9–10 and the flags in Table 3 directly reproducible from the text. I also credit the authors for candidly listing their assumptions and for acknowledging, in Section 5.3, that the Table 3 models are selected on the S Dor strip so that most unstable flags are unsurprising. The strongest quantitative content is in Eqs. 24–26 and Figures 9–10; these are also where the manuscript needs the most work, because the rotating-star trigger convention is stated ambiguously (Major Comment 1). The observational comparison is suggestive rather than decisive, but the paper does not oversell the individual nebular matches.

major comments (4)
  1. [§4.2, Eq. 22; §7, assumption (a)] The paper's rotating-star trigger criterion is internally ambiguous, and the two self-consistent readings differ by up to a factor of about 2 at the rotation rates used in Table 3. For ω = 0 the criterion is g_rad = 0.9 g_N (Eq. 4), i.e., g_N − g_rad = 0.1 g_N. Assumption (a) in Section 7 states that for rotating stars the trigger occurs when "the effective surface gravity is reduced by rotation and radiation pressure to only 10% of the Newtonian gravity," which reads as g_N − Ω²R_eq − g_rad = 0.1 g_N, i.e., g_rad = (0.9 − ω²) g_N. Equation 22 instead sets g_rad = 0.9 g_N (1 − ω²) = 0.9 g_rot, which is the criterion that results if Γ_mod is defined with the rotation-reduced gravity in the denominator, as in the usual ΩΓ-limit treatment. The two conventions agree only at ω = 0; at ω = 0.9 the required g_rad differs by the factor (0.9 − ω²)/[0.9(1 − ω²)] ≈ 0.53, and Eq. 24 changes by the same factor. The paper must adopt one convention explicitly. If the intended convention is the margin relative to Newtonian gravity, Eqs. 22–24 and Figures 9–10 must be recomputed; several borderline cases in Table 3 change (e.g., the Z = 0.014, M_i = 32 M_sun non-rotating model at ω = 0.6, with log(L/M) = 4.021 versus a threshold of log ≈ 4.04, flips from N to Y_eq, and the lone pole-only model at ω = 0.9 becomes unstable at both poles and equator). If, instead, the intended convention is Γ_mod = g_rad/g_rot = 0.9, then Eq. 22 can stand but the wording of Section 4 ("10% of the gravity") and of assumption (a) must be corrected, and the paper should justify why the UF98 non-rotating calibration carries over to that ratio. The qualitative conclusions (equator-first, strip broadening) survive under either reading, but the quantitative thresholds are not uniquely determined as written.
  2. [§5.1–5.3, Table 3; Abstract] The abstract's claim that the numerical models "confirm that most LBVs should be unstable at both the equator and the poles" is stronger than the model construction can support. The parameters in Table 3 are chosen at the first post-MS crossing of the observed S Dor strip (Section 5.1), and the UF98 instability criterion is calibrated to that same observed strip, so the ω = 0 flags are close to tautological. The authors acknowledge this in Section 5.3, noting that it is "not surprising" that most models are unstable; I weigh that admission in their favor. The genuine content of Table 3 is the differential, rotation-dependent behavior: which models change stability flags between ω = 0 and ω = 0.9, the equator-versus-pole ordering, and the inferred disk/bipolar classification. I recommend that the abstract, Section 6, and Section 7 be repositioned around these differential predictions rather than around the fraction of unstable models, which is built in by construction.
  3. [§3.2, Eqs. 6–8 and 24–26] The opacity function κ_max(T_eff) is taken from UF98 models that individually reach Γ_mod = 0.9 at their respective log g. When Eqs. 24–26 are applied to the equator of a rotating star, the local atmosphere at the trigger satisfies a different radiation-pressure condition (g_rad/g_N = 0.9(1 − ω²) or (0.9 − ω²), depending on the convention chosen in Major Comment 1) and has a local effective gravity lower than the polar value, so the same κ_max(T) curve is being used outside the conditions under which it was computed. In addition, several equatorial temperatures in Table 3 fall below the 10,000 K lower bound of the fitted f(T_eff) in Eq. A1 (notably T_eq = 8,870 K for the Z = 0.014, M_i = 32 M_sun model at ω = 0.9), so those stability flags rest on extrapolated opacity. Since the threshold values in Figures 9–10 and the flags in Table 3 are the paper's main quantitative output, I ask for a quantitative sensitivity estimate, or an explicit bounding statement, for the effect of the log g dependence and of the extrapolation.
  4. [§2.2, Table 2, §5.2] The adopted present-day rotation rates ω = 0.6 and 0.9 are not reached by the evolutionary tracks used to select the models: Table 2 gives ω ≤ 0.065 at the TAMS for the Z = 0.014 models and ω ≤ 0.465 for Z = 0.002, and Section 4.2 shows that ω decreases as the star expands (ω ∝ T_eff). The high-ω columns of Table 3 are therefore a parameter study, not an evolutionary prediction; they are observationally motivated by fast rotators such as AG Car and HR Car, but those cases require a spin-up channel (merger or anisotropic mass loss, Section 2.2) that is not modeled. The paper should state this distinction explicitly, and the quantitative predictions at ω = 0.6–0.9 (including the disk/bipolar morphology claims) should be flagged as contingent on the assumed spin-up mechanism.
minor comments (7)
  1. [Table 3, Z=0.014 no-rot, M_i=60] The entry v_esc(eq) = 1689 km s⁻¹ for the ω = 0.9 row is inconsistent with v_esc(p) = 223 km s⁻¹ and with the listed v∞(p)/v∞(eq) = 2.64; the stated bistability factors (2.6 and 1.3) imply v_esc(eq) ≈ 169 km s⁻¹, so this appears to be a typographical error.
  2. [Table 3, v∞(p)/v∞(eq) column] The v∞(p)/v∞(eq) column should be checked against the stated 2.6/1.3/0.7 bistability factors; for example, the Z = 0.014 no-rot, M_i = 32 M_sun, ω = 0.9 row (T_p ≈ 15,900 K, T_eq ≈ 8,870 K) should yield a ratio of about 4.0 (factors 1.3 and 0.7), not the listed 1.97.
  3. [§4.2, Eqs. 22–26] The equations mix masses: ω is defined via Ω_crit with the effective mass M_eff (Eq. 11), while the trigger criteria use the full mass M (with electron scattering folded into κ_max, per the footnote to Eq. 3); a sentence explaining the intended use of M versus M_eff would remove ambiguity.
  4. [§5.2, Table 3] State explicitly which model rows rely on the f(T_eff) polynomial outside its fitted range of 10,000–60,000 K (Eq. A1), and give the associated uncertainty for those stability flags.
  5. [Abstract and §6] The abstract's phrase "dense equatorial disks or rings and high-velocity bipolar outflows" states as a model output what the paper actually infers from instability flags and v∞ ratios without a mass-loss or hydrodynamical calculation; suggest softening the wording.
  6. [Throughout] Typos and minor defects: "corresond" (Section 6), "occurence" (Section 7), "instabiltiy" (Section 5.2), "criterium" (throughout), a stray "1" after Eq. 3, and broken spacing in Table 3 entries such as "30 7" and "319 31 9".
  7. [§3.1, Eq. 4] The sensitivity of the results to the adopted threshold Y_max = 0.9 is not discussed; since (L/M)_crit scales linearly with Y_max, a one-line statement (e.g., Y_max = 0.8 shifts the curves in Fig. 9 by about 0.05 dex) would help the reader judge the robustness of Table 3.

Circularity Check

1 steps flagged · score 4.0 of 10

Rotation-dependent threshold is genuinely derived; the 'most LBVs unstable' result is partly built into the strip-based model selection.

  1. fitted input called prediction [Section 5.1 (model selection) and Section 5.3, final paragraph]
    "We realize that the stellar parameters of the models in Table 3 were chosen in such a way that they are, by definition, at or very close to the S Dor strip. Therefore it is not surprising to find that most models are unstable at their equator even at small values of omega."

    The model LBVs' L, M, and Tmean are not drawn from an independent grid; they are adopted at the point where Geneva tracks 'first cross the S Dor instability strip' (Section 5.1). The S Dor strip is independently identified as the locus where Gamma_mod is approximately 0.8-0.9 (Section 3.1, UF98 calibration), and the instability criterion in Eqs. 4 and 24 is the same Gamma_mod = 0.9 condition. Placing models on the Gamma_mod ~ 0.9 strip therefore almost guarantees they satisfy the Gamma_mod = 0.9 instability criterion. The authors concede this explicitly.

full rationale

The rotation-dependent core of the paper is not circular. Equations 22-26 combine the adopted UF98 threshold with the von Zeipel gravity-darkening relation (Eq. 17) and the total-to-polar luminosity ratio Psi(omega) (Eq. 15) to derive a critical L/M that scales as Psi(omega)/kappa_max(T). The equator-first ordering and the broadening of the instability strip with omega follow from Teq < Tp and kappa_max(Teq) > kappa_max(Tp), not from the threshold itself. The UF98 Gamma_mod = 0.9 trigger is an external calibration, and the paper is explicit that it is adopted rather than derived. The one partially circular element is the numerical 'confirmation' that most LBV models are unstable: the models' parameters are chosen where Geneva tracks first cross the S Dor strip (Section 5.1), which is the same Gamma_mod ~ 0.9 locus used to calibrate the criterion; the authors acknowledge this in Section 5.3. That makes the abstract's 'confirm that most LBVs should be unstable' partly a selection effect, but it does not infect the rotation-dependent predictions, which have independent content. The skeptic's Eq. 22 concern is a consistency issue rather than a circularity: applying the 0.9 factor to the rotation-reduced gravity instead of to Newtonian gravity as stated in Section 7(a) shifts the quantitative thresholds (by up to a factor ~0.53 at omega = 0.9) and can change individual Table 3 flags, but this is an internal inconsistency, not a reduction of the output to the input. No load-bearing self-citations or imported uniqueness theorems are present.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The analysis borrows its trigger threshold, opacity tables, evolutionary initial conditions, wind scaling, and rigid-rotation geometry from prior work. The new content is the combination of these pieces into rotating-star instability criteria, plus the parameter grid. No new physical entities are postulated.

free parameters (2)
  • Ymax = 0.9 instability threshold = 0.9
    Adopted from UF98's comparison with the LBV strip; all instability flags in Table 3 depend on this threshold, and the paper does not derive it independently.
  • Power-law fit coefficients in Eqs. A1-A4 = Coefficients listed in Appendix A
    Fitted to UF98 LTE opacity data and to the numerically computed rotating-star shape and surface area; accuracies are quoted as 0.002 to 0.007 and they are auxiliary approximations, not tuned to the LBV sample.
assumptions (7)
  • domain assumption The S Dor instability is triggered when the effective surface gravity is reduced to 10 percent of Newtonian gravity, Gamma_mod = 0.9 (UF98).
    Adopted in Section 3, Eq. 3, and listed as assumption (a) in Section 7. All instability predictions follow from this threshold.
  • domain assumption The atmosphere's radiation pressure is set by the maximum Rosseland mean opacity kappa_max in 10^-2 < tau < 10^3, computed from LTE ATLAS9 model atmospheres by UF98.
    Used throughout via Eq. 6 and the power-law fits in Eq. A1; the rotating star's stability is evaluated by comparing kappa_max at Teq and Tp.
  • standard math Von Zeipel's theorem: the local radiative flux is proportional to the local effective gravity (F proportional to g_eff).
    Used to derive the Teq/Tp ratio in Eq. 17 and to connect local temperatures to local gravity.
  • domain assumption Rotation is rigid: Omega is independent of latitude, and the stellar shape is described by the Roche model with sub-photospheric opacity equal to electron scattering.
    Section 4.1, Eqs. 9-13. The paper explicitly ignores differential rotation and magnetic fields.
  • domain assumption During post-main-sequence expansion at nearly constant mass, the envelope conserves angular momentum, so Omega scales as R^-2 and omega scales as R^-1/2.
    Section 4.2, Eq. 21 and Fig. 8. The numerical models nevertheless adopt fixed omega values independently of this scaling.
  • domain assumption Wind terminal velocity scales with local escape velocity, with empirical bistability ratios v_infinity/v_esc = 2.6, 1.3, and 0.7 depending on Teff.
    Section 5.2, Eq. 28 and following text. This turns instability flags into predicted disk and bipolar geometries.
  • domain assumption The total luminosity and surface-averaged mean temperature Tmean from Geneva evolutionary tracks characterize the star independent of rotational distortion; the polar radius is derived from L, Tmean, and surface area.
    Section 5.2: the paper states it implicitly assumes the total surface at that evolution phase is independent of the rotationally distorted shape.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The Effect of Rotation on Triggering S Doradus Instabilities in Luminous Blue Variables." pith.science (2026). https://pith.science/paper/V5ZYUFCZ

@misc{pith2026250209504,
  author       = {Pith},
  title        = {Pith review of: The Effect of Rotation on Triggering S Doradus Instabilities in Luminous Blue Variables},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V5ZYUFCZ}},
  note         = {Machine review of arXiv:2502.09504}
}
read the original abstract

Luminous blue variables are an intermediate stage in the evolution of high-mass stars characterized by extreme mass loss and substantial variability. The stars show large irregular episodic variations on timescales of years to decades in these stars' effective temperatures (called "S Dor variations"). Observations show that these variations are triggered when the stars are in a well-defined strip in the HRD that corresponds to the Modified Eddington Limit, where the atmospheric radiation pressure almost balances gravity. In this work we consider the role that rotation plays in the instability that leads to the triggering of S Dor variations in luminous post-main sequence LBVs. We adopt the existing instability criterion that the effective surface gravity is reduced to 10% of the Newtonian gravity due to radiation pressure in the atmosphere of non-rotating stars. We then specifically describe how rotation impacts this instability. By carrying out numerical simulations of model LBVs at both solar and sub-solar metallicities, we confirm that most LBVs should be unstable at both the equator and the poles, and that rotation exacerbates this effect; some models also produce enhanced mass loss at the pole or equator. Our numerical models also predict dense equatorial disks or rings and high-velocity bipolar outflows, in agreement with existing observations of LBV circumstellar nebulae.

Figures

Figures reproduced from arXiv: 2502.09504 by the authors.

Figure 1
Figure 1. The location on the HRD of LBVs from [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. The location in the HRD of LMC and SMC LBVs in their hot phase is compared with their predicted location for various values of grad/gN. The solid line is the LBV instability strip. The dashed line is the location where grad/gN = 0.90. The location where several values of this parameter (0.80, 0.89, and 0.92) are reached on the LBV-strip are indicated with short horizontal lines. 3.2. The value of κ max UF98 have cal… view at source ↗
Figure 3
Figure 3. Upper panel: The function f(Teff ) = gE/gN for the atmospheric models of Z = 0.02 and 0.002 and X = 0.74 that reach Γmod = 0.90 (from UF98). Lower panel: The maximum values of the atmospheric absorption coefficient in the optical depth range of 10−2 < τ < 103 in atmospheric models of Z = 0.02 and 0.002 and XH = 0.74 that reach Γmod = 0.90, derived by UF98. The dashed line shows the electron scattering coefficient σe… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: The function k(Z, T, XH) for Z = 0.02 (full lines) and Z = 0.002 (dotted lines) for various values of XH. geff(Θ) =h GMeff R2(Θ) + Ω2R(Θ)sin2 (Θ)2 + Ω4R 2 (Θ)sin2 (Θ)cos2 (Θ)i1/2 (9) where Ω is the angular velocity. The first term in Eq. 9 is the Newtonian gravity, c…
Figure 5
Figure 5. Figure 5: Properties of rotating stars as a function of ω. Top: the ratio Req/Rp as a function of ω. Middle: the ratio Teq 4 /Tp 4 between the radiative fluxes at the equator and the pole. Bottom: The function Ψ(ω) = Ltot/Lp. Req/Rp = 1 + 0.5ω 2 (12) The ratio Req/Rp is shown in…
Figure 6
Figure 6. Figure 6: The radiative flux F(Θ)/F(0) as a function of the co-latitude Θ for several values of ω. geff(π/2) = GMeff/Req 2 − Ω 2Req = GMeff/Req 2 (1 − ω 2 ) (16) at the equator. This results in a ratio (Teq/Tp) 4 = (Rp/Req) 2 (1 − ω 2 ) = (1 − ω 2 ) (1 + 0.5ω2) 2 (17) where the …
Figure 7
Figure 7. Figure 7: The ratios Tp/Tmean (top) and Teq/Tmean (bottom) as a function of ω, where Tmean is the value of the effective temperature for a rotating star, defined by Eq. 18 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: The variation of Ω as function of R during the post-MS expansion of rotating stars of Mi = 32, 40, 60 and 85 M⊙ with metallicity Z = 0.002 predicted by Georgy et al. (2013). The models have an initial rotation rate of ω = Ω/Ωcrit = 0.4. The straight line in the upper r…
Figure 9
Figure 9. Figure 9: The dependence of (L/M)crit on T for rotating models of XH = 0.74 and values of ω=0 (black), 0.3 (green), 0.6 (blue) and 0.9 (red). Full lines are for Z = 0.02 and dashed lines for Z = 0.002. For XH < 0.74 the values of log(L/M)crit have to be corrected by a factor log…
Figure 10
Figure 10. Figure 10: The predicted critical values of L/M, where the equator of a rotating star becomes unstable as a function of the mean temperature Tmean = Teff , for XH = 0.74 and Z = 0.02 (upper panel) and 0.002 (lower panel) and for different rotation rates ω = 0 (black), 0.3 (green…
Figure 11
Figure 11. Figure 11: Locations of our model LBVs on the HRD, as compared to the non-rotating (left) and rotating (right) Geneva evolutionary models for solar (top) and SMC (bottom) metallicity. The location of the S Dor instability strip is overplotted in grey; the parameters for our mode…
Figure 12
Figure 12. Figure 12: The effect of rotation on stability for stellar models with Galactic metallicity (listed in [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]
Figure 13
Figure 13. Figure 13: As in [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

72 extracted references · 45 canonical work pages

  1. [1]

    F., & Drout, M

    Aadland, E., Massey, P., Neugent, K. F., & Drout, M. R. 2018, AJ, 156, 294, doi: 10.3847/1538-3881/aaeb96

    doi:10.3847/1538-3881/aaeb96 2018

  2. [2]

    1986, in Luminous Stars and Associations in Galaxies, ed

    Appenzeller, I. 1986, in Luminous Stars and Associations in Galaxies, ed. C. W. H. De Loore, A. J. Willis, & P. Laskarides, Vol. 116, 139–148

    work page 1986

  3. [3]

    1989, in Astrophysics and Space Science

    Appenzeller, I. 1989, in Astrophysics and Space Science

    work page 1989

  4. [4]

    The stability of late-type stars close to the Eddington limit

    Asplund, M. 1998, A&A, 330, 641, doi: 10.48550/arXiv.astro-ph/9710158

    work page Pith review arXiv doi:10.48550/arxiv.astro-ph/9710158 1998

  5. [5]

    L., et al

    Bodensteiner, J., Sana, H., Dufton, P. L., et al. 2023, A&A, 680, A32, doi: 10.1051/0004-6361/202345950

    doi:10.1051/0004-6361/202345950 2023

  6. [6]

    J., et al

    Burggraf, B., Weis, K., Bomans, D. J., et al. 2015, A&A, 581, A12, doi: 10.1051/0004-6361/201323308

    work page doi:10.1051/0004-6361/201323308 2015

  7. [7]

    S., & Negueruela, I

    Clark, J. S., & Negueruela, I. 2004, A&A, 413, L15, doi: 10.1051/0004-6361:20031700

    work page doi:10.1051/0004-6361:20031700 2004

  8. [8]

    Crowther, P. A. 1997, in Astronomical Society of the Pacific Conference Series, Vol. 120, Luminous Blue Variables: Massive Stars in Transition, ed. A. Nota & H. Lamers, 51

    work page 1997

Show all 72 references
  1. [9]

    1987, ApJ, 317, 760, doi: 10.1086/165324 —

    Davidson, K. 1987, ApJ, 317, 760, doi: 10.1086/165324 —. 2020, Galaxies, 8, 10, doi: 10.3390/galaxies8010010

    1987 doi

  2. [10]

    M., & Weis, K

    Davidson, K., Humphreys, R. M., & Weis, K. 2016, arXiv e-prints, arXiv:1608.02007, doi: 10.48550/arXiv.1608.02007 24

    2016 doi arXiv

  3. [11]

    D., & Vink, J

    Davies, B., Oudmaijer, R. D., & Vink, J. S. 2005, A&A, 439, 1107, doi: 10.1051/0004-6361:20052781 de Koter, A., Lamers, H. J. G. L. M., & Schmutz, W. 1996, A&A, 306, 501

    2005 doi

  4. [12]

    Z., Levesque, E

    Dorn-Wallenstein, T. Z., Levesque, E. M., Neugent, K. F., et al. 2020, ApJ, 902, 24, doi: 10.3847/1538-4357/abb318

    2020 doi

  5. [13]

    Z., Neugent, K

    Dorn-Wallenstein, T. Z., Neugent, K. F., & Levesque, E. M. 2023, ApJ, 959, 102, doi: 10.3847/1538-4357/ad0725

    2023 doi

  6. [14]

    Eddington, A. S. 1926, The Internal Constitution of the Stars Ekstr¨ om, S., Georgy, C., Eggenberger, P., et al. 2012, A&A, 537, A146, doi: 10.1051/0004-6361/201117751

    1926 doi

  7. [15]

    2013, A&A, 558, A103, doi: 10.1051/0004-6361/201322178

    Georgy, C., Ekstr¨ om, S., Eggenberger, P., et al. 2013, A&A, 558, A103, doi: 10.1051/0004-6361/201322178

    2013 doi

  8. [16]

    R., et al

    Gootkin, K., Dorn-Wallenstein, T., Lomax, J. R., et al. 2020, ApJ, 900, 162, doi: 10.3847/1538-4357/abad32 Gr¨ afener, G., & Hamann, W. R. 2008, in Revista Mexicana de Astronomia y Astrofisica Conference Series, Vol. 33, Revista Mexicana de Astronomia y Astrofisica Conference Se...

    2020 doi

  9. [17]

    L., Bigley, A., Mauerhan, J

    Graham, M. L., Bigley, A., Mauerhan, J. C., et al. 2017, MNRAS, 469, 1559, doi: 10.1093/mnras/stx948

    2017 doi

  10. [18]

    2021, A&A, 647, A99, doi: 10.1051/0004-6361/202038298

    Grassitelli, L., Langer, N., Mackey, J., et al. 2021, A&A, 647, A99, doi: 10.1051/0004-6361/202038298

    2021 doi

  11. [19]

    H., Hillier, D

    Groh, J. H., Hillier, D. J., & Damineli, A. 2006, ApJL, 638, L33, doi: 10.1086/500928

    2006 doi

  12. [20]

    H., Damineli, A., Hillier, D

    Groh, J. H., Damineli, A., Hillier, D. J., et al. 2009, ApJL, 705, L25, doi: 10.1088/0004-637X/705/1/L25

    2009 doi

  13. [21]

    H., Ekstr¨ om, S., Georgy, C., et al

    Groh, J. H., Ekstr¨ om, S., Georgy, C., et al. 2019, A&A, 627, A24, doi: 10.1051/0004-6361/201833720

    2019 doi

  14. [22]

    Holgado, G., Sim´ on-D ´ ıaz, S., Herrero, A., & Barb´ a, R. H. 2022, A&A, 665, A150, doi: 10.1051/0004-6361/202243851

    2022 doi

  15. [23]

    R., & McSwain, M

    Huang, W., Gies, D. R., & McSwain, M. V. 2010, ApJ, 722, 605, doi: 10.1088/0004-637X/722/1/605

    2010 doi

  16. [24]

    W., Wang, C., et al

    Huang, Y., Zhang, H. W., Wang, C., et al. 2019, ApJL, 884, L7, doi: 10.3847/2041-8213/ab430b

    2019 doi

  17. [25]

    M., & Davidson, K

    Humphreys, R. M., & Davidson, K. 1979, ApJ, 232, 409, doi: 10.1086/157301 —. 1994, PASP, 106, 1025, doi: 10.1086/133478

    1979 doi

  18. [26]

    M., Weis, K., Davidson, K., & Gordon, M

    Humphreys, R. M., Weis, K., Davidson, K., & Gordon, M. S. 2016, ApJ, 825, 64, doi: 10.3847/0004-637X/825/1/64

    2016 doi

  19. [27]

    2018, Nature, 561, 498, doi: 10.1038/s41586-018-0525-0

    Jiang, Y.-F., Cantiello, M., Bildsten, L., et al. 2018, Nature, 561, 498, doi: 10.1038/s41586-018-0525-0

    2018 doi

  20. [28]

    2022, MNRAS, 517, 2028, doi: 10.1093/mnras/stac2598

    Keszthelyi, Z., de Koter, A., G¨ otberg, Y., et al. 2022, MNRAS, 517, 2028, doi: 10.1093/mnras/stac2598

    2022 doi

  21. [29]

    P., Pauldrach, A., Puls, J., & Abbott, D

    Kudritzki, R. P., Pauldrach, A., Puls, J., & Abbott, D. C. 1989, A&A, 219, 205

    1989

  22. [30]

    Kurucz, R. L. 1995, Highlights of Astronomy, 10, 407

    1995

  23. [31]

    Lamers, H. J. G. L. M. 1986, in IAU Symposium, Vol. 116, Luminous Stars and Associations in Galaxies, ed. C. W. H. De Loore, A. J. Willis, & P. Laskarides, 157–178

    1986

  24. [32]

    Lamers, H. J. G. L. M. 1989, in Astrophysics and Space Science Library, Vol. 157, IAU Colloq. 113: Physics of Luminous Blue Variables, ed. K. Davidson, A. F. J. Moffat, & H. J. G. L. M. Lamers, 135

    1989

  25. [33]

    Lamers, H. J. G. L. M. 1995, in Astronomical Society of the Pacific Conference Series, Vol. 83, IAU Colloq. 155: Astrophysical Applications of Stellar Pulsation, ed. R. S. Stobie & P. A. Whitelock, 176

    1995

  26. [34]

    Lamers, H. J. G. L. M., & Cassinelli, J. P. 1999, Introduction to Stellar Winds, 452

    1999

  27. [35]

    Lamers, H. J. G. L. M., & Cassinelli, J. P. 1999, Introduction to Stellar Winds (Cambridge University Press). https://ui.adsabs.harvard.edu/abs/1999isw..book.....L

    1999

  28. [36]

    Lamers, H. J. G. L. M., & Fitzpatrick, E. L. 1988, ApJ, 324, 279, doi: 10.1086/165894

    1988 doi

  29. [37]

    Lamers, H. J. G. L. M., & Noordhoek, R. 1993, in Astronomical Society of the Pacific Conference Series, Vol. 35, Massive Stars: Their Lives in the Interstellar Medium, ed. J. P. Cassinelli & E. B. Churchwell, 517

    1993

  30. [38]

    Lamers, H. J. G. L. M., Snow, T. P., & Lindholm, D. M. 1995, ApJ, 455, 269, doi: 10.1086/176575

    1995 doi

  31. [39]

    1997, in Astronomical Society of the Pacific Conference Series, Vol

    Langer, N. 1997, in Astronomical Society of the Pacific Conference Series, Vol. 120, Luminous Blue Variables: Massive Stars in Transition, ed. A. Nota & H. Lamers, 83

    1997

  32. [40]

    1997, in Astronomical Society of the Pacific Conference Series, Vol

    Leitherer, C. 1997, in Astronomical Society of the Pacific Conference Series, Vol. 120, Luminous Blue Variables: Massive Stars in Transition, ed. A. Nota & H. Lamers, 58

    1997

  33. [41]

    Bally, J., & Keeney, B. A. 2014, AJ, 147, 23, doi: 10.1088/0004-6256/147/1/23

    2014 doi

  34. [42]

    2002, A&A, 392, 575, doi: 10.1051/0004-6361:20020938 —

    Maeder, A. 2002, A&A, 392, 575, doi: 10.1051/0004-6361:20020938 —. 2009, Physics, Formation and Evolution of Rotating Stars, doi: 10.1007/978-3-540-76949-1

    2002 doi

  35. [43]

    M., et al

    Margutti, R., Milisavljevic, D., Soderberg, A. M., et al. 2014, ApJ, 780, 21, doi: 10.1088/0004-637X/780/1/21

    2014 doi

  36. [44]

    C., & Humphreys, R

    Martin, J. C., & Humphreys, R. M. 2023, AJ, 166, 214, doi: 10.3847/1538-3881/ad011e

    2023 doi

  37. [45]

    2023, ApJ, 942, 69, doi: 10.3847/1538-4357/aca665

    Meynet, G. 2023, ApJ, 942, 69, doi: 10.3847/1538-4357/aca665

    2023 doi

  38. [46]

    H., et al

    Mehner, A., Baade, D., Groh, J. H., et al. 2017, A&A, 608, A124, doi: 10.1051/0004-6361/201731829

    2017 doi

  39. [47]

    2021, A&A, 655, A33, doi: 10.1051/0004-6361/202141473

    Mehner, A., Janssens, S., Agliozzo, C., et al. 2021, A&A, 655, A33, doi: 10.1051/0004-6361/202141473

    2021 doi

  40. [48]

    1997, A&A, 321, 465 25

    Meynet, G., & Maeder, A. 1997, A&A, 321, 465 25

    1997

  41. [49]

    P., Hirai, R., Podsiadlowski, P., & Schneider, F

    Owocki, S. P., Hirai, R., Podsiadlowski, P., & Schneider, F. R. N. 2019, MNRAS, 485, 988, doi: 10.1093/mnras/stz461

    2019 doi

  42. [50]

    P., & Shaviv, N

    Owocki, S. P., & Shaviv, N. J. 2016, MNRAS, 462, 345, doi: 10.1093/mnras/stw1642

    2016 doi

  43. [51]

    P., Townsend, R

    Owocki, S. P., Townsend, R. H. D., & Quataert, E. 2017, MNRAS, 472, 3749, doi: 10.1093/mnras/stx2251

    2017 doi

  44. [52]

    R., Baade, D., et al

    Reilly, E., Maund, J. R., Baade, D., et al. 2017, MNRAS, 470, 1491, doi: 10.1093/mnras/stx1228

    2017 doi

  45. [53]

    D., & Mehner, A

    Richardson, N. D., & Mehner, A. 2018, Research Notes of the American Astronomical Society, 2, 121, doi: 10.3847/2515-5172/aad1f3

    2018 doi

  46. [54]

    W., Clark, J

    Ritchie, B. W., Clark, J. S., Negueruela, I., & Najarro, F. 2009, A&A, 507, 1597, doi: 10.1051/0004-6361/200912986

    2009 doi

  47. [55]

    Schneider, F. R. N., Langer, N., de Koter, A., et al. 2014, A&A, 570, A66, doi: 10.1051/0004-6361/201424286

    2014 doi

  48. [56]

    J., & Howarth, I

    Harries, T. J., & Howarth, I. D. 1994, ApJ, 429, 846, doi: 10.1086/174369

    1994 doi

  49. [57]

    E., Leitherer, C., Clayton, G

    Schulte-Ladbeck, R. E., Leitherer, C., Clayton, G. C., et al . 1993, ApJ, 407, 723, doi: 10.1086/172553

    1993 doi

  50. [58]

    2002, MNRAS, 336, L22, doi: 10.1046/j.1365-8711.2002.05964.x

    Smith, N. 2002, MNRAS, 336, L22, doi: 10.1046/j.1365-8711.2002.05964.x

    2002

  51. [59]

    2015, MNRAS, 447, 598, doi: 10.1093/mnras/stu2430

    Smith, N., & Tombleson, R. 2015, MNRAS, 447, 598, doi: 10.1093/mnras/stu2430

    2015 doi

  52. [60]

    S., & de Koter, A

    Smith, N., Vink, J. S., & de Koter, A. 2004, ApJ, 615, 475, doi: 10.1086/424030

    2004 doi

  53. [61]

    Spoon, H. W. W., de Koter, A., Sterken, C., Lamers, H. J. G. L. M., & Stahl, O. 1994, A&AS, 106, 141

    1994

  54. [62]

    2003, A&A, 400, 279, doi: 10.1051/0004-6361:20021908

    Stahl, O., G¨ ang, T., Sterken, C., et al. 2003, A&A, 400, 279, doi: 10.1051/0004-6361:20021908

    2003 doi

  55. [63]

    2001, A&A, 375, 54, doi: 10.1051/0004-6361:20010824

    Stahl, O., Jankovics, I., Kov´ acs, J., et al. 2001, A&A, 375, 54, doi: 10.1051/0004-6361:20010824

    2001 doi

  56. [64]

    M., Davidson, K., et al

    Szeifert, T., Humphreys, R. M., Davidson, K., et al. 1996, A&A, 314, 131

    1996

  57. [65]

    Ulmer, A., & Fitzpatrick, E. L. 1998, ApJ, 504, 200, doi: 10.1086/306048 van Genderen, A. M. 2001, A&A, 366, 508, doi: 10.1051/0004-6361:20000022

    1998 doi

  58. [66]

    Vink, J. S. 2012, in Astrophysics and Space Science

    2012

  59. [67]

    S., & de Koter, A

    Vink, J. S., & de Koter, A. 2002, A&A, 393, 543, doi: 10.1051/0004-6361:20021009

    2002 doi

  60. [68]

    S., de Koter, A., & Lamers, H

    Vink, J. S., de Koter, A., & Lamers, H. J. G. L. M. 1999, A&A, 350, 181 —. 2001, A&A, 369, 574, doi: 10.1051/0004-6361:20010127

    1999 doi

  61. [69]

    S., & Gr¨ afener, G

    Vink, J. S., & Gr¨ afener, G. 2012, ApJL, 751, L34, doi: 10.1088/2041-8205/751/2/L34

    2012 doi

  62. [70]

    S., Muijres, L

    Vink, J. S., Muijres, L. E., Anthonisse, B., et al. 2011, A&A, 531, A132, doi: 10.1051/0004-6361/201116614 von Zeipel, H. 1924, MNRAS, 84, 665, doi: 10.1093/mnras/84.9.665

    2011 doi

  63. [71]

    Weis, K., & Bomans, D. J. 2020, Galaxies, 8, 20, doi: 10.3390/galaxies8010020

    2020 doi

  64. [72]

    1989, A&A, 217, 87 26 Table 3

    Wolf, B. 1989, A&A, 217, 87 26 Table 3. Parameters of rotating stars in the S Dor instability strip Mi M log(L) log(L/M) log( Tmean) XH ω R p Req log(Tp) log( Teq) vrot(eq) vesc(p) vesc(eq) Instab? v∞(p)/v ∞(eq) (M⊙) ( M⊙) ( L⊙) ( L⊙/M⊙) K ( R⊙) ( R⊙) (K) (K) (km/s) (km/s) (km...

    1989

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.