Pith. sign in

REVIEW 3 major objections 4 minor 57 references

Massive stars host brief habitable zones at tens to hundreds of AU, yet add about a hundred thousand Earth analogues at a time.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-02 23:22 UTC pith:4IR7ZVVQ

load-bearing objection Qualitative result is robust, but the headline 9 Msun, 30-Myr MS HZ is not reproducible as written because the atmospheric survival time tau is unstated and contradicts the figure caption. the 3 major comments →

arxiv 2602.13875 v2 pith:4IR7ZVVQ submitted 2026-02-14 astro-ph.SR astro-ph.EPastro-ph.GA

Habitable Zones Around Massive Stars: From the Main Sequence to Supergiants

Devesh Nandal , Abraham Loeb This is my paper
classification astro-ph.SR astro-ph.EPastro-ph.GA
keywords massive starshabitable zoneatmospheric escapestellar windsXUV irradiationplanet habitabilitystellar evolutionEarth analogues
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper sets out to replace a presumption—that massive stars' UV fields and winds rule out Earth-like habitability—with a quantified, time-resolved answer. It computes habitable-zone annuli for solar-metallicity stars from 0.8 to 120 solar masses, using stellar evolution tracks plus three inner-edge limits (runaway greenhouse, XUV-driven escape, wind ram pressure). The central finding is a sharp main-sequence ceiling: habitability persists for about 30 Myr at 9 solar masses near 70–130 AU, becomes a brief narrow band by 12 solar masses, and vanishes by 15 solar masses; post-main-sequence evolution reopens zones up to 25–30 solar masses for only ~0.03–1.5 Myr. Weighted by a Milky-Way-like initial mass function (IMF), massive stars contribute only ~1e-4 of the habitable planet-time budget, yet still amount to a few hundred thousand Earth analogues at any instant. The result matters because it turns a demographic question about the Galaxy's habitable worlds into concrete numbers and identifies short-lived wide-orbit targets for biosignature searches.

Core claim

The paper's central claim is that an 'operational' habitable zone—defined not only by bolometric climate limits but by the planet's ability to retain an atmosphere against XUV-driven escape and wind ram pressure—has a sharp upper mass boundary on the main sequence. The annulus exists essentially for the full main-sequence lifetime up to about 9 solar masses, with radii ~74–127 AU and duration ~31 Myr; by 12 solar masses it shrinks to a ~1-Myr sliver around 256–263 AU; by 15 solar masses no main-sequence annulus forms. After core-hydrogen exhaustion, higher-mass stars can briefly re-open a habitable zone (up to ~25–30 solar masses, for 0.03–1.5 Myr at hundreds to ~1000 AU), but not above ~40

What carries the argument

The operational habitable zone is the central object: an annulus whose outer edge is the standard bolometric climate bound and whose inner edge is the most restrictive of three limits—the runaway-greenhouse bolometric edge, an extreme-ultraviolet (XUV) energy-limited atmospheric escape edge, and a wind ram-pressure edge evaluated against a dipole-magnetized Earth analogue. The XUV and wind edges are the load-bearing parts; they scale with stellar luminosity, radius, effective temperature, mass-loss rate, and a two-branch wind terminal speed that jumps at the bi-stability temperature. These terms steepen and become more time-variable with stellar mass until the annulus collapses to zero width

Load-bearing premise

The whole mass ceiling rests on the adopted XUV luminosity and wind terminal speeds, which are estimated from a blackbody XUV fraction and a two-branch v∞ scaling; in real massive stars XUV is non-thermal and winds are clumped and variable, so if these inputs are off by factors of a few, the ~10–15 solar-mass main-sequence ceiling and ~30 solar-mass post-main-sequence limit shift—as the paper's final section itself notes.

What would settle it

Measure the XUV luminosity and wind momentum (Mdot v∞) for a sample of late-O to early-B stars (around 9–15 solar masses) and compare with the blackbody + bi-stability prescriptions used here. If the true LXUV(t) or Mdot v∞ is systematically a factor of ~2–3 different, recomputing the XUV and wind inner edges would move or erase the claimed main-sequence ceiling; a direct measurement therefore settles whether a 12-solar-mass star can or cannot host a sustained operational habitable zone.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A 9-solar-mass star sustains an operational main-sequence habitable zone for ~30 Myr at ~70–130 AU; by 12 solar masses the zone becomes a brief, narrow annulus, and by 15 solar masses none exists.
  • Post-main-sequence evolution reopens habitable zones for stars up to ~25–30 solar masses, but only for ~0.03–1.5 Myr at hundreds to ~1000 AU, and they vanish above ~40 solar masses.
  • Under Milky-Way-like IMFs, massive stars contribute only ~1e-4 of the total habitable planet-time budget; including them changes the Galaxy-wide total by ~1e-4.
  • In absolute terms, massive-star systems still add on the order of 1.5–3.5e5 Earth analogues at any instant if wide-orbit rocky planets form and survive there.
  • Transit surveys cannot reach these zones (periods of ~10^2–10^3 yr), and reflected-light contrast is prohibitive; thermal mid-infrared observations are the plausible channel.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If real O/B stars emit most of their XUV non-thermally (shock-heated winds) and their winds are clumped and time-variable, the blackbody-based inner edge could shift; a factor-of-few change in LXUV or Mdot v_inf would move the 10–15 solar-mass main-sequence ceiling and the ~30 solar-mass post-MS limit.
  • Super-Earth-mass planets with more massive atmospheres would push the escape-limited inner edge inward, possibly broadening the narrow transition around 10–12 solar masses.
  • Wide-orbit HZ planets around massive stars must form or migrate to tens to hundreds of AU before external photoevaporation and dynamical heating in OB clusters erase their disks; the absolute counts are therefore upper limits unless formation-and-survival physics is included.
  • In high-redshift or top-heavy IMF environments, where massive stars are relatively more numerous, their ~1e-4 share of planet-time could grow, so cosmic history may be more favorable than the present-day Milky Way.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper couples rotating and non-rotating Geneva GENEC stellar tracks (0.8–120 M_sun, Z=0.014) to three time-dependent HZ boundaries—bolometric climate limits, XUV energy-limited escape, and wind ram-pressure standoff—and defines an “operational HZ” whose inner edge is the most restrictive of the three. It computes annulus-existence times, fixed-orbit residence times, planet-multiplicity bounds, and IMF-weighted yields. The headline claims are a sharp main-sequence ceiling (9 M_sun has a ~30-Myr HZ at ~70–130 AU; 12 M_sun is brief and narrow; 15 M_sun has none), a post-MS reopening up to ~25–30 M_sun, and a Milky-Way inventory in which massive stars contribute only ~10^-4 of the habitable planet–time budget but nonetheless add a few 10^5 instantaneous Earth analogues. The qualitative direction is plausible, but the quantitative ceiling and the multiplicity/yield numbers are not reproducible as written.

Significance. The question addressed—whether massive stars can host any operational habitable annulus once XUV and wind erosion are included—is well motivated and under-explored. The paper makes a useful contribution by combining published GENEC tracks with retention-limited inner edges, exploring a parameter grid for escape and magnetospheric parameters, and connecting the results to detectability and IMF-weighted demographics. The qualitative conclusion that massive stars contribute only ~10^-4 of the habitable-planet-time budget is likely robust to the details. However, the central quantitative claim, a sharp 9–12 M_sun main-sequence ceiling, depends on an unstated and internally inconsistent choice of the exposure time τ, and the multiplicity estimates in §2.4/Fig. 3 cannot be reproduced from the stated equations. These issues are load-bearing for the paper's headline numbers, so the manuscript needs substantial revision before the quantitative results can be accepted.

major comments (3)
  1. [§2.2.2–2.2.4, Fig. 1 caption, Table 1] The fiducial τ used for Tables 1–2 is never stated, while the Fig. 1 caption says r_XUV is computed with τ=0.1 Myr. For the 9 M_sun track (T_eff≈20,000–22,000 K), Eqs. (7)–(9) with the stated constants give r_XUV/r_out,clim ≈ sqrt(61.3 f_XUV) ≈ 1.1–1.4 for τ=0.1 Myr (with Planck f_XUV≈0.02–0.03), i.e. r_XUV exceeds r_out,clim and no MS annulus should exist. Table 1 instead reports Δt_HZ,MS=31.06 Myr with ⟨r_in⟩/⟨r_out⟩≈0.58, which requires τ≈0.03 Myr. The reported values are therefore not reproducible from the stated method, and the headline 9 M_sun window depends on an unstated choice of τ.
  2. [§2.3, Eq. (14), §3.2] The “sustains a ~30 Myr HZ” claim conflates annulus existence with atmospheric survival. The XUV inner edge Eq. (9) only sets r_XUV such that at that radius the integrated energy-limited loss equals M_atm after an exposure τ. If Table 1 effectively uses τ≈0.03 Myr, then at the outer edge (a=r_out≈127 AU, r_XUV≈74 AU) the loss timescale is τ(r_out/r_XUV)^2≈0.09 Myr; no orbit in the annulus retains its atmosphere for 30 Myr. The residence-time diagnostic in §3.2 checks only geometric containment r_in(t)<a<r_out(t); it does not integrate XUV mass loss along the orbit. Thus the 30-Myr MS window is an annulus-existence statement, not a retention/survival statement, and the abstract's wording is unsupported.
  3. [§2.4.2, Fig. 3, Table 2] The reported Method B multiplicities cannot be reproduced from the stated equations. For the 1 M_sun track, Table 1 gives r_in=0.982, r_out=1.686 AU; with p=0, a_min=0.1, a_max=100 in Eq. (20), f_HZ≈0.007. With M_dust,⊙=50 M⊕, f_rock=0.5, ε_form=0.5, M_avail≈0.088 M⊕, below M_min=0.1 M⊕, so N=0 by the stated floor(M_avail/M_min). Yet Fig. 3 reports N_MS=8 (K=12) for 0.9–7 M_sun. For 9 M_sun, the stated stellar-mass-scaled M_dust gives M_p≈6 M⊕ for N=10, μ≈0.011, γ≈1.19 (K=16), N_space≈4, not 7. The reported spike appears to require an unstated modification (e.g., unscaled 50 M⊕ reservoir), and the Method B yields in Table 2 are therefore not supported by the written methods.
minor comments (4)
  1. [§3, first paragraph] “We being by mapping” should read “We begin by mapping”.
  2. [Fig. 3 caption] Method A is defined in §2.4.1 by period-ratio R=1.33, not by K=12; the K notation in the left-panel caption should be removed or defined consistently.
  3. [Eq. (20)] When r_out exceeds a_max, the numerator should be truncated at a_max; otherwise f_HZ counts solids outside the adopted reservoir. For several high-mass models r_out >100 AU, this changes the computed M_avail.
  4. [Tables 1–2] The parameter tuple (τ, ε, B_p, R_crit) used for the fiducial results should be stated explicitly in the table captions or in a dedicated paragraph in §2.5. Currently the fiducial values for all four parameters are not identified.

Circularity Check

0 steps flagged

No significant circularity: the mass ceiling and IMF yields follow from stated evolutionary tracks and prescribed retention formulas, not from fitting or self-referential definitions.

full rationale

The derivation chain is self-contained and non-circular. The operational inner edge (Eq. 14) is the max of three independently stated constraints: bolometric climate (Eq. 5, Kopparapu constants), XUV energy-limited escape (Eq. 9 with blackbody L_XUV from Eqs. 7-8), and wind ram pressure (Eq. 13 with a Vink-like two-branch terminal speed). No parameter in these formulas is fitted to the headline MS ceiling; the 9 to 15 M_sun ceiling emerges from the ratios r_XUV/r_out and r_wind/r_out, whose mass dependence comes from T_eff, Mdot, and v_inf on published GENEC tracks. The GENEC tracks are cited to Nandal et al. (2023, 2024) but are externally published evolutionary models with stated assumptions, not constructed to encode the HZ result. The multiplicity and IMF-weighted yields are computed by forward formulas (Eqs. 16-25) and are normalization-dependent rather than circular: changing f_rock, eps_form, a_max, or occurrence factor changes absolute numbers but not the derivation logic. The paper's own Section 5 limitation statement (XUV/wind prescriptions are the main uncertainty) is a model-uncertainty caveat, not an admission that the result is assumed. One internal-consistency issue, the Fig. 1 caption's tau=0.1 Myr appears inconsistent with Table 1's wide MS annuli if Eqs. 7-9 are evaluated with that tau, is a numerical/parameter-reporting concern, not a circular reduction, and does not change the circularity verdict.

Axiom & Free-Parameter Ledger

12 free parameters · 8 axioms · 0 invented entities

No new physical entities are introduced. The paper combines standard stellar evolution, climate-HZ, energy-limited escape, and wind-pressure models; its headline numbers depend on a set of fiducial or grid-sampled parameters rather than on a new force, particle, or conserved quantity.

free parameters (12)
  • S_eff,in / S_eff,out = 1.015 / 0.35
    Fixed bolometric climate thresholds from Kopparapu (2013), used without spectral correction in Eq. 5.
  • Wind terminal-speed parameters: eta_hot, eta_cool, T_bist = 2.6 / 1.3 / 21,000 K
    Two-branch bi-stability scaling from Vink et al. (2001), used in Eq. 4 to compute r_wind.
  • XUV heating efficiency epsilon = grid {0.05, 0.1, 0.3}
    Energy-limited escape efficiency in Eq. 9; strongly controls r_XUV and the MS ceiling.
  • Exposure time tau = grid {0.01, 0.03, 0.1, 0.3, 1, 3, 10} Myr; Fig. 1 uses 0.1 Myr
    Integration time for atmospheric removal in Eq. 9; a free timescale.
  • Surface magnetic field B_p = fiducial 0.3 G; grid {0.1, 0.3, 1.0} G
    Dipole field strength of the Earth analogue used in wind ram-pressure balance.
  • Magnetopause standoff R_crit = fiducial 2.5; grid {2.0, 2.5, 5.0}
    Dimensionless magnetopause distance in Eqs. 10–11.
  • Atmosphere mass M_atm = 5e18 kg
    Fixed Earth-like atmosphere mass to be removed by XUV escape.
  • Disk solids normalization M_dust,sun = 50 M_Earth
    Solids reservoir scale for multiplicity Model B, Eq. 19.
  • Rocky fraction f_rock and formation efficiency eps_form = 0.5 / 0.5 (sensitivity +-30%)
    Parameters in Eq. 21 converting solids reservoir into planet mass.
  • Disk and packing parameters: p, a_min, a_max, K, R, M_min = p=0; a_min=0.1 AU; a_max=100/1000 AU; K in {12,16,20}; R=1.33; M_min=0.1 M_Earth
    Radial solids weighting, disk bounds, Hill spacing, minimum period ratio, and minimum planet mass in Eqs. 16–22.
  • Occurrence factor eta_Earth and Milky Way SFR = 0.1 / 1.9 M_sun/yr
    Normalization in Eq. 26 converting yield into an instantaneous Galactic count; not fitted but arbitrary.
  • Initial rotation rate v_ini/v_crit = 0.4
    Rotating GENEC grid choice; compared against non-rotating grid.
axioms (8)
  • domain assumption Stellar XUV luminosity is approximated by a Planck blackbody over 10–118 nm (Eqs. 7–8)
    Massive-star XUV is shock-heated and non-thermal; this proxy is acknowledged but not calibrated to observations.
  • domain assumption Energy-limited escape with a fixed atmosphere mass and no replenishment sets r_XUV (Eq. 9)
    Standard formula, but ignores replenishment, chemistry, and magnetic suppression of escape.
  • domain assumption Wind ram pressure Mdot v_inf/(4 pi a^2) with v_inf = eta(T_eff) v_esc balances a dipolar magnetopause (Eqs. 2–4, 10–13)
    CAK-style parameterization from Vink et al.; ignores wind variability and clumping.
  • domain assumption Climate HZ is pure bolometric with fixed S_eff thresholds (Eq. 5)
    No spectral correction or cloud/UV feedback; unverified for hot stars.
  • domain assumption GENEC solar-metallicity tracks accurately provide L, T_eff, Mdot, and lifetimes
    All time evolution is taken from these tracks; systematic mass-loss errors propagate into r_wind and the ceiling.
  • domain assumption Earth-analog terrestrial planets can form and survive at 70–1000 AU
    Required for the absolute 'few 1e5 Earth analogues' count; the paper states this as conditional.
  • standard math Kepler scaling and mutual-Hill stability bound multi-planet packing (Eqs. 16–18)
    Standard orbital mechanics and N-body-motivated stability criteria from the cited literature.
  • domain assumption Salpeter, Kroupa, and Chabrier IMFs and a steady SFR describe the Milky Way population
    Needed for IMF-weighted yields and the Galactic normalization.

pith-pipeline@v1.3.0-alltime-deepseek · 21437 in / 17786 out tokens · 153102 ms · 2026-08-02T23:22:54.796492+00:00 · methodology

0 comments
read the original abstract

Massive stars dominate the feedback of young stellar populations, yet their ultraviolet fields and winds are often presumed to preclude Earth like habitability. We test this by mapping time dependent habitable zones (HZs) for solar metallicity stars of $0.8$--$120\,M_\odot$. Using rotating and non rotating \textsc{GENEC} tracks, we compute bolometric climate HZ boundaries and impose XUV energy limited escape and wind ram pressure constraints for a dipole-magnetized Earth analogue. The retention limited inner edge is the most restrictive limit. We measure annulus lifetime, longest fixed orbit residence, and maximum dynamically packed terrestrial multiplicity, finding a sharp main-sequence ceiling. A rotating $9\,M_\odot$ star sustains a retention limited HZ for $\sim 30$ Myr at $\sim 70$--$130$ AU, but becomes brief and narrow by $12\,M_\odot$ and disappears by $15\,M_\odot$. Post main-sequence evolution can reopen HZs up to $\sim 25$--$30\,M_\odot$, but only for $\sim 0.03$--$1.5$ Myr at hundreds to $\sim 10^3$ AU, disappearing by $\sim 40\,M_\odot$. Stellar rotation modestly increases habitable lifetimes near the upper main sequence without altering the high mass ceiling. IMF weighting shows that massive stars contribute only $\sim 10^{-4}$ of the habitable planet time budget. Even so, for the fiducial occurrence normalization and if rocky planets form or survive at the required wide separations, they add a few $10^5$ Earth analogues satisfying the adopted criteria to the Milky Way at any instant. Massive star systems do not dominate the Galaxy-wide habitability budget, but may provide short-lived, distinct targets for biosignature searches.

Figures

Figures reproduced from arXiv: 2602.13875 by Abraham Loeb, Devesh Nandal.

Figure 1
Figure 1. Figure 1: Time evolution of habitable-zone radii for six rotating solar-metallicity GENEC tracks (0.8, 1, 5, 9, 15, and 25 M⊙; model identifiers are shown in the upper-left of each panel). The climate-only inner and outer boundaries are rin,clim (green dashed) and rout,clim (orange), while the adopted inner edge is rin = max(rin,clim, rwind, rXUV) (blue); rwind (magenta dashed) and rXUV (purple dashed, computed for … view at source ↗
Figure 2
Figure 2. Figure 2: Existence time and maximum fixed-orbit resi￾dence time versus initial mass for the rotating solar-metallic￾ity GENEC grid. Solid curves show the cumulative HZ exis￾tence durations ∆tHZ and dashed curves show the maximum contiguous residence time ∆tres = maxa ∆t(a), each eval￾uated separately on the MS and post-MS. Horizontal lines indicate benchmark residence requirements. and finally NMS = 0 for Mini ≥ 12… view at source ↗
Figure 3
Figure 3. Figure 3: Maximum HZ planet multiplicity inferred from [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Rotation versus non-rotation comparison of HZ boundary evolution at 9 M⊙ (left) and 20 M⊙ (right). Blue curves show non-rot S0 models and red curves show rot S0.4 models. Solid curves plot the operational inner edge rin,op(t) and dashed curves plot the climate outer edge rout,clim(t). Thin horizontal lines mark the residence-orbit locations ares in each phase. Top panels use MS age. Bottom panels use time … view at source ↗
Figure 5
Figure 5. Figure 5: Grid-wide rotation sensitivity of habitable time budgets and the residence orbit. Left panel shows 100 (∆tHZ,rot − ∆tHZ,nonrot)/tMS,nonrot for MS and post-MS phases. Right panel shows 100 [ares,rot/ares,nonrot − 1] for MS and post-MS phases. Vertical dotted lines mark Mini = 9 and 20 M⊙, matching the detailed comparisons in [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: shows the IMF weighted habitability-yield density, dY /d log10 Mini (per dex), for the P. Kroupa (2001) IMF, with color distinguishing S0 and S0.4 and line style distinguishing Method A from Method B. Each point gives the yield density associated with an initial-mass bin, plotted at the log-midpoint of the bin; multiplying by the bin width ∆ log10 M recovers that bin’s contribution to the total Y . The mas… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

57 extracted references · 8 canonical work pages · 1 internal anchor

  1. [1]

    S., Barnes, R., Cohen, O., et al

    Airapetian, V. S., Barnes, R., Cohen, O., et al. 2020, International Journal of Astrobiology, 19, 136, doi: 10.1017/S1473550419000132

    doi:10.1017/s1473550419000132 2020

  2. [2]

    S., Angerhausen, D., et al

    Alei, E., Konrad, B. S., Angerhausen, D., et al. 2022, Astronomy & Astrophysics, 665, A106, doi: 10.1051/0004-6361/202243760

    doi:10.1051/0004-6361/202243760 2022

  3. [3]

    M., Rosenfeld, K

    Andrews, S. M., Rosenfeld, K. A., Kraus, A. L., & Wilner, D. J. 2013, ApJ, 771, 129, doi: 10.1088/0004-637X/771/2/129

    doi:10.1088/0004-637x/771/2/129 2013

  4. [4]

    J., Koch, D

    Borucki, W. J., Koch, D. G., Brown, T. M., et al. 2010, ApJL, 713, L126, doi: 10.1088/2041-8205/713/2/L126

    doi:10.1088/2041-8205/713/2/l126 2010

  5. [5]

    E., Cantiello, M., et al

    Brott, I., de Mink, S. E., Cantiello, M., et al. 2011, A&A, 530, A115, doi: 10.1051/0004-6361/201016113

    doi:10.1051/0004-6361/201016113 2011

  6. [6]

    I., Abbott, D

    Castor, J. I., Abbott, D. C., & Klein, R. I. 1975, ApJ, 195, 157, doi: 10.1086/153315

    doi:10.1086/153315 1975

  7. [7]

    2003, PASP, 115, 763, doi: 10.1086/376392

    Chabrier, G. 2003, PASP, 115, 763, doi: 10.1086/376392

    doi:10.1086/376392 2003

  8. [8]

    E., Wetherill, G

    Chambers, J. E., Wetherill, G. W., & Boss, A. P. 1996, Icarus, 119, 261, doi: 10.1006/icar.1996.0019

    arXiv 1996

  9. [9]

    1931, Proceedings of the Physical Society, 43, 26, doi: 10.1088/0959-5309/43/1/305

    Chapman, S. 1931, Proceedings of the Physical Society, 43, 26, doi: 10.1088/0959-5309/43/1/305

    work page doi:10.1088/0959-5309/43/1/305 1931

  10. [10]

    Crowther, P. A. 2007, ARA&A, 45, 177, doi: 10.1146/annurev.astro.45.051806.110615

    Pith/arXiv arXiv 2007

  11. [11]

    C., & Lopez, B

    Danchi, W. C., & Lopez, B. 2013, ApJ, 769, 27, doi: 10.1088/0004-637X/769/1/27

    doi:10.1088/0004-637x/769/1/27 2013

  12. [12]

    J., Contardo, G., Sandoval, A., et al

    David, T. J., Contardo, G., Sandoval, A., et al. 2021, AJ, 161, 265, doi: 10.3847/1538-3881/abf439

    doi:10.3847/1538-3881/abf439 2021

  13. [13]

    2008, Ap&SS, 316, 43, doi: 10.1007/s10509-007-9511-y Ekstr¨ om, S., Georgy, C., Eggenberger, P., et al

    Eggenberger, P., Meynet, G., Maeder, A., et al. 2008, Ap&SS, 316, 43, doi: 10.1007/s10509-007-9511-y Ekstr¨ om, S., Georgy, C., Eggenberger, P., et al. 2012, A&A, 537, A146, doi: 10.1051/0004-6361/201117751

    doi:10.1007/s10509-007-9511-y 2008

  14. [14]

    C., & Loeb, A

    Forbes, J. C., & Loeb, A. 2018, MNRAS, 479, 171, doi: 10.1093/mnras/sty1433

    doi:10.1093/mnras/sty1433 2018

  15. [15]

    A., Vanderburg, A., Rodriguez, J

    Gilbert, E. A., Vanderburg, A., Rodriguez, J. E., et al. 2023, ApJL, 944, L35, doi: 10.3847/2041-8213/acb599

    doi:10.3847/2041-8213/acb599 2023

  16. [16]

    1993, Icarus, 106, 247, doi: 10.1006/icar.1993.1169 Grießmeier, J.-M., Stadelmann, A., Penz, T., et al

    Gladman, B. 1993, Icarus, 106, 247, doi: 10.1006/icar.1993.1169 Grießmeier, J.-M., Stadelmann, A., Penz, T., et al. 2004, A&A, 425, 753, doi: 10.1051/0004-6361:20035684

    arXiv 1993

  17. [17]

    Hart, M. H. 1979, Icarus, 37, 351, doi: 10.1016/0019-1035(79)90141-6

    work page doi:10.1016/0019-1035(79)90141-6 1979

  18. [18]

    1959, PASP, 71, 421, doi: 10.1086/127417

    Huang, S.-S. 1959, PASP, 71, 421, doi: 10.1086/127417

    work page doi:10.1086/127417 1959

  19. [19]

    1960, PASP, 72, 489, doi: 10.1086/127586

    Huang, S.-S. 1960, PASP, 72, 489, doi: 10.1086/127586

    work page doi:10.1086/127586 1960

  20. [20]

    1998, ApJ, 499, 758, doi: 10.1086/305658

    Johnstone, D., Hollenbach, D., & Bally, J. 1998, ApJ, 499, 758, doi: 10.1086/305658

    doi:10.1086/305658 1998

  21. [21]

    Kaltenegger, L., & Faherty, J. K. 2021, Nature, 594, 505, doi: 10.1038/s41586-021-03596-y

    work page doi:10.1038/s41586-021-03596-y 2021

  22. [22]

    2011, ApJL, 736, L25, doi: 10.1088/2041-8205/736/2/L25

    Kaltenegger, L., & Sasselov, D. 2011, ApJL, 736, L25, doi: 10.1088/2041-8205/736/2/L25

    work page doi:10.1088/2041-8205/736/2/l25 2011

  23. [23]

    F., Whitmire, D

    Kasting, J. F., Whitmire, D. P., & Reynolds, R. T. 1993, Icarus, 101, 108, doi: 10.1006/icar.1993.1010

    arXiv 1993

  24. [24]

    Kopparapu, R. K. 2013, ApJL, 767, L8, doi: 10.1088/2041-8205/767/1/L8

    doi:10.1088/2041-8205/767/1/l8 2013

  25. [25]

    K., Ramirez, R

    Kopparapu, R. K., Ramirez, R. M., SchottelKotte, J., et al. 2014, ApJL, 787, L29, doi: 10.1088/2041-8205/787/2/L29

    doi:10.1088/2041-8205/787/2/l29 2014

  26. [26]

    2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x

    Kroupa, P. 2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x

    arXiv 2001

  27. [27]

    Krumholz, M. R. 2014, PhR, 539, 49, doi: 10.1016/j.physrep.2014.02.001

    doi:10.1016/j.physrep.2014.02.001 2014

  28. [28]

    Kudritzki, R. P. 2002, ApJ, 577, 389, doi: 10.1086/342178

    doi:10.1086/342178 2002

  29. [29]

    2003, ApJL, 598, L121, doi: 10.1086/380815

    Lammer, H., Selsis, F., Ribas, I., et al. 2003, ApJL, 598, L121, doi: 10.1086/380815

    doi:10.1086/380815 2003

  30. [30]

    2012, ARA&A, 50, 107, doi: 10.1146/annurev-astro-081811-125534 Lecavelier Des Etangs, A

    Langer, N. 2012, ARA&A, 50, 107, doi: 10.1146/annurev-astro-081811-125534 Lecavelier Des Etangs, A. 2007, A&A, 461, 1185, doi: 10.1051/0004-6361:20065014

    doi:10.1146/annurev-astro-081811-125534 2012

  31. [31]

    2021, Life in the Cosmos: From Biosignatures to Technosignatures

    Lingam, M., & Loeb, A. 2021, Life in the Cosmos: From Biosignatures to Technosignatures

    2021

  32. [32]

    2016, ApJL, 819, L21, doi: 10.3847/2041-8205/819/2/L21

    Loeb, A. 2016, ApJL, 819, L21, doi: 10.3847/2041-8205/819/2/L21

    doi:10.3847/2041-8205/819/2/l21 2016

  33. [33]

    Lopez, B., Schneider, J., & Danchi, W. C. 2005, ApJ, 627, 974, doi: 10.1086/430416

    work page doi:10.1086/430416 2005

  34. [34]

    1997, A&A, 321, 134

    Maeder, A. 1997, A&A, 321, 134

    1997

  35. [35]

    W., Mawet, D., Ruffio, J.-B., et al

    McElwain, M. W., Mawet, D., Ruffio, J.-B., et al. 2025, arXiv e-prints, arXiv:2510.02547, doi: 10.48550/arXiv.2510.02547

    doi:10.48550/arxiv.2510.02547 2025

  36. [36]

    Single massive stars at the critical rotational velocity: possible links with Be and B[e] stars

    Meynet, G., & Maeder, A. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 355, Stars with the B[e] Phenomenon, ed. M. Kraus & A. S. Miroshnichenko, 27, doi: 10.48550/arXiv.astro-ph/0511269

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/0511269 2006

  37. [37]

    A., Woods, T

    Nandal, D., Regan, J. A., Woods, T. E., et al. 2023, A&A, 677, A155, doi: 10.1051/0004-6361/202346938

    doi:10.1051/0004-6361/202346938 2023

  38. [38]

    2024, A&A, 684, A169, doi: 10.1051/0004-6361/202346979

    Nandal, D., Meynet, G., Ekstr¨ om, S., et al. 2024, A&A, 684, A169, doi: 10.1051/0004-6361/202346979

    doi:10.1051/0004-6361/202346979 2024

  39. [39]

    E., Clarke, C

    Owen, J. E., Clarke, C. J., & Ercolano, B. 2012, MNRAS, 422, 1880, doi: 10.1111/j.1365-2966.2011.20337.x

    arXiv 2012

  40. [40]

    Parker, E. N. 1958, ApJ, 128, 664, doi: 10.1086/146579

    doi:10.1086/146579 1958

  41. [41]

    2025, A&A, 694, A179, doi: 10.1051/0004-6361/202452580

    Pezzotti, C., Buldgen, G., Magaudda, E., et al. 2025, A&A, 694, A179, doi: 10.1051/0004-6361/202452580

    doi:10.1051/0004-6361/202452580 2025

  42. [42]

    S., & Najarro, F

    Puls, J., Vink, J. S., & Najarro, F. 2008, A&A Rv, 16, 209, doi: 10.1007/s00159-008-0015-8

    doi:10.1007/s00159-008-0015-8 2008

  43. [43]

    P., Ottiger, M., Fontanet, E., et al

    Quanz, S. P., Ottiger, M., Fontanet, E., et al. 2022, A&A, 664, A21, doi: 10.1051/0004-6361/202140366

    doi:10.1051/0004-6361/202140366 2022

  44. [44]

    M., & Kaltenegger, L

    Ramirez, R. M., & Kaltenegger, L. 2016, ApJ, 823, 6, doi: 10.3847/0004-637X/823/1/6

    doi:10.3847/0004-637x/823/1/6 2016

  45. [45]

    2014, Experimental Astronomy, 38, 249, doi: 10.1007/s10686-014-9383-4 17

    Rauer, H., Catala, C., Aerts, C., et al. 2014, Experimental Astronomy, 38, 249, doi: 10.1007/s10686-014-9383-4 17

    doi:10.1007/s10686-014-9383-4 2014

  46. [46]

    R., Winn, J

    Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, Journal of Astronomical Telescopes, Instruments, and Systems, 1, 014003, doi: 10.1117/1.JATIS.1.1.014003

    doi:10.1117/1.jatis.1.1.014003 2015

  47. [47]

    J., Claire, M

    Rushby, A. J., Claire, M. W., Osborn, H., & Watson, A. J. 2013, Astrobiology, 13, 833, doi: 10.1089/ast.2012.0938

    arXiv 2013

  48. [48]

    Salpeter, E. E. 1955, ApJ, 121, 161, doi: 10.1086/145971

    doi:10.1086/145971 1955

  49. [49]

    F., Levrard, B., et al

    Selsis, F., Kasting, J. F., Levrard, B., et al. 2007, A&A, 476, 1373, doi: 10.1051/0004-6361:20078091

    doi:10.1051/0004-6361:20078091 2007

  50. [50]

    A., Jardine, M., Morin, J., et al

    Vidotto, A. A., Jardine, M., Morin, J., et al. 2013, A&A, 557, A67, doi: 10.1051/0004-6361/201321504

    doi:10.1051/0004-6361/201321504 2013

  51. [51]

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

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

    doi:10.1051/0004-6361:20010127 2001

  52. [52]

    J., Donahue, T

    Watson, A. J., Donahue, T. M., & Walker, J. C. G. 1981, Icarus, 48, 150, doi: 10.1016/0019-1035(81)90101-9

    doi:10.1016/0019-1035(81)90101-9 1981

  53. [53]

    P., & Cieza, L

    Williams, J. P., & Cieza, L. A. 2011, ARA&A, 49, 67, doi: 10.1146/annurev-astro-081710-102548

    doi:10.1146/annurev-astro-081710-102548 2011

  54. [54]

    2022, MNRAS, 515, 4287, doi: 10.1093/mnras/stac1564

    Nayakshin, S. 2022, MNRAS, 515, 4287, doi: 10.1093/mnras/stac1564

    doi:10.1093/mnras/stac1564 2022

  55. [55]

    C., Zhou, J.-L., & Steffen, J

    Wu, D.-H., Zhang, R. C., Zhou, J.-L., & Steffen, J. H. 2019, MNRAS, 484, 1538, doi: 10.1093/mnras/stz054

    doi:10.1093/mnras/stz054 2019

  56. [56]

    C., & Abbot, D

    Yang, J., Bou´ e, G., Fabrycky, D. C., & Abbot, D. S. 2014, ApJL, 787, L2, doi: 10.1088/2041-8205/787/1/L2

    doi:10.1088/2041-8205/787/1/l2 2014

  57. [57]

    Zinnecker, H., & Yorke, H. W. 2007, ARA&A, 45, 481, doi: 10.1146/annurev.astro.44.051905.092549

    Pith/arXiv arXiv 2007