Evolutionary tracks, ejecta, and ionizing photons from intermediate-mass to very massive stars with PARSEC

A. Bressan; A. Mazzi; C. T. Nguyen; D. Bossini; F. Addari; G. Costa; G. Pastorelli; G. Volpato; K. G. Shepherd; L. Girardi

REVIEW 3 major objections 3 minor 3 cited by

Evolutionary tracks, ejecta, and ionizing photons from intermediate-mass to very massive stars with PARSEC

T0 review · 3 major / 3 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A new set of stellar evolution models predicts that single stars leave no black holes between about 100 and 130 solar masses, a far narrower pair-instability gap than standard estimates.

desk verdict A valuable PARSEC v2.0 data release whose headline mass-gap edges are more fragile than the abstract admits; the grid itself deserves refereed publication. read the letter →

arxiv 2501.12917 v2 pith:ME75UKLA submitted 2025-01-22 astro-ph.SR astro-ph.GAastro-ph.HE

G. Costa , K. G. Shepherd , A. Bressan , F. Addari , Y. Chen , X. Fu , G. Volpato , C. T. Nguyen

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L. Girardi P. Marigo A. Mazzi G. Pastorelli M. Trabucchi D. Bossini S. Zaggia

This is my paper · ORCID

classification astro-ph.SRastro-ph.GAastro-ph.HE MSC 85A15 PACS 97.10.Cv97.60.Bw97.60.Lf

keywords stellarevolutionpair-instabilitysupernovaeblackholemassgapconvectivedredge-upverymassivestarsionizingphotonschemicalyieldsPARSECmodels

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 presents a new, homogeneous grid of stellar evolution models computed with the PARSEC v2.0 code, covering initial masses from 2 to 2000 solar masses across thirteen metallicities from primordial to super-solar. Its central claim is that, for single stars, the pair-instability black-hole mass gap, the range of black-hole masses that no single-star collapse should produce, is much narrower than previously thought, about 100 to 130 solar masses rather than roughly 50 to 140 solar masses. The narrowing is driven by deep convective dredge-up episodes that shave down helium core masses and keep some stars from entering the pair-instability regime. The same models reproduce the masses of observed black holes such as the GW190521 primary, Cygnus X-1, and Gaia BH3, and provide new tables of chemical ejecta and ionizing-photon rates. If correct, the result reshapes predictions for gravitational-wave sources and for the most massive remnants single stars can leave behind.

What carries the argument

The helium-core mass $M_{\mathrm{He}}$ at the pre-supernova stage is the organizing quantity: PARSEC v2.0 evolves each star with an implicit diffusive mixing scheme that couples nuclear burning and element transport, using the Schwarzschild convection criterion with core overshooting $\lambda_{\rm ov}=0.5$ (about 0.25 pressure scale heights) and envelope overshooting $\Lambda_{\rm env}=0.7\,H_P$. Deep convective dredge-up during core helium burning can push the base of the convective envelope into the helium core, reducing $M_{\mathrm{He}}$ and $M_{\mathrm{CO}}$; the paper identifies these episodes, not just winds, as the reason the pair-instability gap narrows. Final fates, namely core-collapse supernova, failed supernova, pulsational pair-instability supernova, pair-instability supernova, or direct collapse, are assigned by mapping the computed $M_{\mathrm{He}}$ and $M_{\mathrm{CO}}$ onto remnant and ejecta tables, with the Stothers criterion $\langle\Gamma_1\rangle < 4/3$ marking entry into the pair-instability regime.

What would settle it

Detect a single-star-born black hole with a mass between 100 and 130 $M_\odot$, for example from a gravitational-wave event whose progenitor is shown to be a single star rather than a merger or accretion product, and the gap is not that narrow. Alternatively, rerun the same grid with an independently calibrated convective mixing scheme and check whether any 80 to 140 $M_\odot$ model still produces a helium core below the pair-instability threshold; if none does, the gap widens.

Watch

Extended reading notes

Core claim

The paper claims that, when all metallicities are combined, no single star leaves a black hole with mass between roughly 100 and 130 $M_\odot$; this combined pair-instability mass gap is far narrower than the $\sim 50$ to $\sim 140$ $M_\odot$ range predicted in previous studies. The narrowing is traced to convective dredge-up episodes: during central helium burning the base of the convective envelope can penetrate the helium core, lowering $M_{\mathrm{He}}$ and $M_{\mathrm{CO}}$ by enough to keep stars that would otherwise explode as pair-instability supernovae stable, so they end as failed supernovae or direct-collapse black holes. The same models place the most massive single-star black hole below the gap at about 99.5 $M_\odot$ at $Z=10^{-11}$ and reproduce the masses inferred for GW190521, Cygnus X-1, and Gaia BH3. The models also predict pulsational pair-instability and pair-instability supernovae at near-solar metallicity, contrasting with the usual assumption that such events require very low metallicity.

Load-bearing premise

The central result depends on the assumed convective mixing recipe, core overshooting of about a quarter of a pressure scale height plus envelope overshooting of 0.7 pressure scale heights, because deeper mixing than real would shrink helium cores too much, pulling the gap edges together, while weaker mixing would probably widen the gap.

Editorial extensions

If this is right

There should be no single-star black holes with masses between about 100 and 130 $M_\odot$ in the local universe, so gravitational-wave events with a primary in that range require exotic formation channels.
GW190521's roughly 85 $M_\odot$ primary can be produced by a low-metallicity single star, with the lower edge of the gap reaching about 76.5 $M_\odot$ at $Z=0.001$.
Pulsational pair-instability and full pair-instability supernovae can occur at near-solar metallicity, so future surveys such as LSST may find these events in metal-rich environments.
The models place the maximum black-hole mass at solar and galactic metallicity around $40\pm6$ $M_\odot$, consistent with Cygnus X-1 and with several other evolutionary codes.
The public grids of stellar tracks, ejecta, and ionizing photons give population-synthesis and galaxy-formation models a homogeneous input from 2 to 2000 $M_\odot$ across thirteen metallicities.

Reading between the lines

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

Beyond the paper, the width of the 100 to 130 $M_\odot$ gap is a prediction of one mixing prescription rather than a theorem, so the gap width should be treated as a test of convective mixing physics, not as a fixed number.
Beyond the paper, because the models are non-rotating, rotation-induced mixing and mass-loss enhancement could shift the effective dredge-up efficiency and move the gap edges by tens of solar masses.
Beyond the paper, binary-stripped stars, which the accompanying pure-helium tracks are designed to serve, could retain enough mass to land inside the 100 to 130 $M_\odot$ range, so the gap is a property of single-star evolution rather than of all black-hole formation channels.
Beyond the paper, asteroseismic or eclipsing-binary measurements of core sizes in red supergiants would provide a direct check of the deep dredge-up geometry assumed here, and a mismatch would be the fastest route to revising the gap.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things you should know. First, this is a major data-release paper: a new homogeneous PARSEC v2.0 grid from 2 to 2000 M_sun across 13 metallicities, plus pure-He tracks, ejecta tables, and ionizing-photon rates, all public. That alone makes it worth having. Second, the central physics claim, a pair-instability mass gap 'just between 100 and 130 M_sun', is a real consequence of the models but is considerably less robust than the abstract's tone suggests; both edges sit on sharp external thresholds applied to mixing-sensitive helium cores.

The genuinely new material is the grid itself and the derived tabulations. The paper does a careful job of documenting the updated input physics, and the comparisons against GENEC, MIST, FRANEC, and the Tarantula/R136 data are honest about where discrepancies arise. The consistency checks with observed BHs (Cyg X-1, Gaia BH3) are a nice sanity check. The public availability of tracks and derived products is a service to the community. Credit is due for the range and homogeneity of the models.

The soft spots are real but not fatal. The abstract and conclusions quote the 100-130 M_sun gap as if it were a settled edge, while the paper itself notes that the pre-SN structure is sensitive to overshooting, mixing, and the choice of external fate mapping (Woosley 2017 via Goswami et al. 2021). The stress-test description is accurate: the lower edge is essentially one track (Z=10^-11, 100 M_sun) that ends with M_He ~33 M_sun, barely below the adopted PPISN threshold, and the upper edge is an interpolation at Z=0.006 where M_He crosses 130 M_sun. With a 10 M_sun step in the 100-300 M_sun range and no variation of mixing parameters or fate thresholds, the precise edges are not established. The paper acknowledges these dependencies in Sec. 3.3 but does not attach uncertainties to the quoted numbers. There is also a clear typo in Table F.1 (a 1000 M_sun star with remnant mass 9993.1 M_sun) and the code itself is not released, only the tracks. These are fixable.

Who should read it: anyone doing population synthesis, gravitational-wave progenitor studies, or galaxy-formation modeling will want these tracks. It deserves a serious referee and a revise-and-resubmit: the data release should go through, but the mass-gap edges need a robustness discussion or an uncertainty estimate, and the table typo should be corrected. I would not hold the central mass-gap claim as a decisive measurement of the gap; it's a model-dependent prediction that should be used with that caveat in mind.

Referee Report

3 major / 3 minor

Summary. This paper releases a new homogeneous grid of non-rotating PARSEC v2.0 stellar evolution tracks covering 2 to 2000 solar masses at thirteen metallicities from Z=10^-11 to Z=0.03. The models are evolved to advanced burning stages or to the onset of the pair instability, and the authors use an external mapping from pre-SN helium and carbon-oxygen core masses to assign final fates and remnant masses. They provide wind and explosive ejecta tables and tabulated ionizing photon rates, and they compare the tracks with other stellar evolution codes and with massive stars in 30 Doradus. The headline physical result is that the combined black-hole pair-instability mass gap across all metallicities is 'just between 100 and 130 M_sun', narrower than previous estimates, which they attribute to deep dredge-up episodes that reduce the helium core mass.

Significance. The grid is a valuable public resource: it is homogeneous, publicly available, and already used in population-synthesis applications, and the accompanying ejecta, ionizing-photon, and pure-He track products extend the PARSEC library in useful ways. The comparisons with MIST, GENEC, FRANEC, and with the Tarantula Nebula data provide a useful benchmark. The external fate mapping is not circular, since it uses independently published grids, but the load-bearing point is that the pre-SN core masses entering that mapping are highly sensitive to the adopted convective mixing treatment. The manuscript does not currently quantify that sensitivity, so the central claim is not yet established at the precision claimed in the abstract; the requested robustness analysis can, however, be accommodated within the scope of a revision.

major comments (3)

[Sec. 3.3, Table 4, App. C] The headline claim that the combined BH pair-instability gap 'spans just between 100 and 130 M_sun' is presented without any uncertainty or robustness analysis, even though both edges are threshold-sensitive. The lower edge (99.5 M_sun) is set by the Z=10^-11, M_ZAMS=100 M_sun model, whose pre-SN M_He=32.96 M_sun sits only a few tenths of a solar mass below the approximately 34 M_sun PPISN threshold; the upper edge (129.4 M_sun at Z=0.006) comes from interpolating the M_He=130 M_sun crossing. Appendix C itself states that small variations can lead to 'big evolutionary differences' and describes the evolution as chaotic. Please add a sensitivity study (for example, varying lambda_ov and Lambda_env, or using alternative fate mappings and threshold choices) or rephrase the abstract and conclusions to present the 100-130 M_sun interval as a model-dependent estimate rather than a precise prediction.
[Sec. 3.3, Table 2] The upper edge of the gap is obtained by interpolating M_He(M_ZAMS) across a mass range where Table 2 has a 10 M_sun step. Since Fig. 5 and Appendix C show that M_He and M_CO are non-monotonic functions of M_ZAMS because of dredge-up, linear interpolation between grid points cannot reliably locate the M_He=130 M_sun crossing; the difference between columns 3 and 4 of Table 4 (up to about 11 M_sun) shows that the interpolation is not a minor correction. Please compute additional tracks around the transition or provide an explicit interpolation uncertainty.
[Sec. 2.1, Sec. 4.1] The deep dredge-up that lowers M_He and closes the gap is controlled by the Schwarzschild criterion, lambda_ov=0.5, and especially Lambda_env=0.7 H_P envelope overshooting. Table 5 shows that other codes adopt substantially different convection parameters, and Section 4.1 compares HR tracks only; it does not validate the final fates or the gap edges. The absence of any test of the mixing parameters leaves the central mass-gap result contingent on an unvalidated prescription. Please either run test models with different overshooting values or explicitly state that the gap edges are conditional on the adopted mixing scheme.

minor comments (3)

[Table F.1] In the Z=10^-11 block, the M_ZAMS=1000 M_sun row lists M_remnant=9993.1 M_sun, which is likely a typo for 999.31 M_sun; in the Z=10^-6 block, the M_ZAMS=2000 M_sun row lists M_remnant=1981.27 M_sun, which exceeds the listed pre-SN mass of 1950.40 M_sun. Please correct these values in the table and in the public database.
[Fig. 1 caption] The caption identifies the center panel as Z=0.001, while the panel label and the text of Sec. 3.1.2 identify it as Z=0.0001; please harmonize the caption with the panel.
[Sec. 2.1] The text uses both 'Schwarzchild' and 'Schwarzschild' for the convective stability criterion; please make the spelling consistent.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; the mass-gap claim emerges from PARSEC tracks via externally sourced final-fate thresholds, with mixing sensitivities noted as robustness caveats rather than circular steps.

full rationale

The paper's central claims (the 100–130 M⊙ combined pair-instability mass gap, remnant masses, ejecta, and ionizing photons) are outputs of full stellar evolution computations, not quantities fitted to the claims. The final-fate mapping uses helium- and carbon-oxygen-core mass thresholds taken from external works: Woosley (2017), Heger & Woosley (2002), Limongi & Chieffi (2003), and Chieffi & Limongi (2004). The Goswami et al. (2021) methodology, though a same-group citation, is used as an interpolation and application procedure; the underlying fate thresholds and remnant-mass tables are external. The low edge of the combined gap (99.5 M⊙ from the Z=10^-11, 100 M⊙ track with MHe≈33 M⊙ just below the PPISN threshold) and the high edge (129.4 M⊙ from interpolating the PISN–DBH transition at MHe≈130 M⊙ for Z=0.006) are derived by applying these external thresholds to computed pre-SN core masses listed in Table F, not by fitting any parameter to reproduce the gap. Self-citations to earlier PARSEC developments (Costa et al. 2019b; Nguyen et al. 2022) and to Costa et al. (2021) for dredge-up are present, but the cited physics is independently implemented in the code, and the central claim is not justified solely by those citations. The paper is also benchmarked externally: comparison with MIST, GENEC, and FRANEC tracks, Tarantula Nebula observations, and observed black holes such as GW190521, Cygnus X-1, and Gaia BH3. Appendix C's statement that the evolution can be 'chaotic' and sensitive to initial conditions is a robustness caveat, not evidence that the derivation is circular. No equation in the paper defines the mass gap in terms of the input parameters by construction, and no fitted quantity is renamed as a prediction. Therefore the circularity score is low.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claims rest on calibrated stellar physics inputs (mixing-length, overshooting, mass-loss efficiencies) and on external mappings from pre-SN core masses to final fates. No new physical entities are introduced. The paper's contribution is a homogeneous grid of models computed with these adopted inputs, not a first-principles derivation.

free parameters (6)

alpha_MLT (mixing length parameter) = 1.74
Calibrated to the solar model (Bressan et al. 2012); adopted for all masses and metallicities in the grid.
lambda_ov (core overshooting parameter) = 0.5 H_P (lov about 0.25 H_P)
Core overshooting choice that controls the size of convective cores and the strength of dredge-up episodes which set the pair-instability mass gap.
Lambda_env (envelope overshooting) = 0.7 H_P
Step overshooting at the base of the convective envelope; affects the extent of blue loops and the depth of dredge-up in massive stars.
eta_R (Reimers mass-loss efficiency) = 0.2
Mass-loss efficiency for RGB and core-helium-burning phases, derived from asteroseismic data (Miglio et al. 2012); adopted as an input calibrator.
Temperature-gradient limit for density inversion = grad T <= 1 - chi_mu grad_mu / chi_T
Ad hoc numerical prescription to prevent density inversions in red supergiant envelopes; changes effective temperatures and radii of RSG tracks.
Pair-instability stability margin = <Gamma_1> threshold = 4/3 + 0.01
Conservative margin added to the Stothers criterion to identify pair-instability; shifts the onset of PI and thus the mass gap edges.

assumptions (4)

domain assumption Stothers criterion <Gamma_1> > 4/3 identifies dynamical instability to pair creation in hydrostatic models (Eq. 2).
Used as the stopping condition for PI; assumes that an adiabatic index average below 4/3 predicts PI onset without full hydrodynamics.
domain assumption Final fates and remnant masses can be mapped from pre-SN M_He and M_CO using external models (Woosley 2017; Limongi & Chieffi 2003, 2004; Heger & Woosley 2002).
The paper does not simulate the explosion; the mass spectrum, including the 100-130 M_sun gap, inherits the assumptions and interpolation of these external grids.
domain assumption Empirical mass-loss prescriptions (Vink et al. 2000, 2001; de Jager et al. 1988; Sander et al. 2019) remain valid when extrapolated to very low metallicity (Z down to 10^-11) and masses up to 2000 M_sun.
The winds shape the final masses and fates, especially at Z >= 0.006; these prescriptions were calibrated on Galactic/LMC stars and their low-Z extension is an unverified extrapolation.
domain assumption The models are non-rotating; rotation-induced mixing and mass loss are neglected.
Stated in Sec. 2; the authors acknowledge rotation can strongly affect massive star evolution, final fates, and ejecta.

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Cite this review

Pith. "Pith review of Evolutionary tracks, ejecta, and ionizing photons from intermediate-mass to very massive stars with PARSEC." pith.science (2026). https://pith.science/paper/ME75UKLA

@misc{pith2026250112917,
  author       = {Pith},
  title        = {Pith review of: Evolutionary tracks, ejecta, and ionizing photons from intermediate-mass to very massive stars with PARSEC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ME75UKLA}},
  note         = {Machine review of arXiv:2501.12917}
}

abstract

Recent advancements in stellar evolution modeling offer unprecedented accuracy in predicting the evolution and deaths of stars. We present new stellar evolutionary models computed with the updated PARSEC V2.0 code for a comprehensive and homogeneous grid of metallicities and initial masses. Nuclear reaction networks, mass loss prescriptions, and the treatment of elemental mixing have all been updated in PARSEC V2.0. We computed models for thirteen initial metallicities spanning $Z = 10^{-11}$ to $Z = 0.03$, with masses ranging from 2.0 M$_{\odot}$ to 2000 M$_{\odot}$, consisting of a library of over 1,100 ($\sim 2100$ tracks including pure-He models) full stellar evolution tracks. For each track, the evolution is followed from the pre-main-sequence to the most advanced early-asymptotic-giant-branch or the pre-supernova phases, depending on the stellar mass. Here, we describe the properties of the tracks and their chemical and structural evolution. We computed the final fates and the remnant masses and built the mass spectrum for each metallicity, finding that the combined black hole (BH) pair-instability mass gap spans just between 100 and 130 M$_{\odot}$. Moreover, the remnant masses provide models consistent with observed BH masses, such as those from the primaries of GW190521, Cygnus X-1, and $\textit{Gaia}$ BH3 binary systems. We computed and provided the chemical ejecta from stellar winds and explosive final fates, along with the ionizing photon rates. Our results show strong overall consistency with other tracks computed with different codes. A comparison with a large sample of observed massive stars in the Tarantula Nebula of the Large Magellanic Cloud shows that our tracks nicely reproduce the majority of stars that lie on the main sequence. All the models are publicly available and can be retrieved on the PARSEC database.

Figures

Figures reproduced from arXiv: 2501.12917 by the authors.

**Figure 1.** HR diagrams of tracks computed with Z = 10−11 , Z = 0.001 and Z = 0.014, in the left-hand, center, and right-hand panels, respectively. Tracks are shown beginning from the ZAMS, indicated by the dashed red line. The dash-dotted black line indicates the TAMS. Blue dots (crosses) indicate the beginning (end) of core helium-burning, respectively. Pink stars indicate the final position of the star. The pre-MS phase is n… view at source ↗

**Figure 2.** Kippenhahn diagrams of stars with MZAMS = 240 M⊙ with metallicity Z = 10−11 (left), Z = 0.001 (center), and Z = 0.014 (right). The black line indicates the total mass of the star. Blue and green lines show the He and CO cores, respectively. Burning zones are indicated in blue, green, and pink for H, He, and C, while the purple hash indicates the convective zones (CZ). The final He core is indicated on each panel. Th… view at source ↗

**Figure 3.** Central (solid) and surface (dashed) abundances as a function of time of a 240 M⊙ star for Z = 10−11 (left), Z = 0.001 (center), and Z = 0.014(right). The abscissa is the time until the last model, and the ordinate is the mass fraction of each element. Light blue, light green, pink, dark blue, purple, dark green, and orange refer to H, 4He, 12C, 14N, 16O, 20Ne + 22Ne, and 24Mg+ 25Mg + 26Mg abundances, respectively. … view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: Mass spectrum of stars with different metallicities in different colors and line styles. The red-shaded area indicates the combined PI mass gap considering all metallicities that experience PI. the collapse are so short that they have negligible effects on the stars’ f…

**Figure 5.** Figure 5: Final fate types for massive stars as a function of initial mass and metallicity. Purple, blue, green, pink, and black indicate the final fate of CCSN, FSN, PPISN, PISN, and DBH, respectively [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: Remnant mass as a function of the initial mass for tracks with Z = 10−6 , Z = 0.002, Z = 0.01, in the top, middle, and bottom panels, respectively. The solid green line indicates the initial mass. The dashed pink, blue, and purple lines indicate the final mass of the s…

**Figure 8.** Figure 8: Total amount of mass ejected for 4 species. Fe refers to the isotopes 52Fe through 51Fe and the 56Ni that decays into 56Fe. It is worth noting the peculiar behavior of 14N for Z = 0.001, resulting from the specific interplay between the dredge-up history and the final…

**Figure 7.** Figure 7: Chemical makeup of ejecta for Z = 0.006 stars. The top panel indicates the total mass lost, the middle is the mass loss due to winds, and the bottom panel shows the sum of the elements from the inner layers ejected (overlayers) plus the explosive ejecta of stars that …

**Figure 9.** Figure 9: HR diagrams of selected Z = 10−11 tracks, color-coded by the log number of ionizing photons emitted per second. From left to right, the panels show the log number of ionizing photons of each type emitted per second (QHI, QHeI, QHeII, QOII, and QLW). Tracks are labeled …

**Figure 10.** Figure 10: Total number of ionizing photons emitted throughout a star’s lifetime as a function of its initial mass and metallicity. Different panels indicate the distinct ionization types considered here. in our sets, using the current mass, stellar radius, effective temperatur…

**Figure 11.** Figure 11: Comparison of non-rotating parsec (green), mist (orange), genec (purple), and franec (blue) tracks in the HR diagram, with MZAMS = 10, 20, 40, 120, and 300 M⊙. Tracks from different codes are computed with the metallicity and input physics parameters listed in [PITH…

**Figure 12.** Figure 12: Comparison between data of stars in the Tarantula Nebula and parsec stellar tracks in the HR diagram. Pink stars and blue dots are from Brands et al. (2022) and Schneider et al. (2018), respectively. Over plotted is the set of tracks with Z = 0.006. The dashed red and…

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Forward citations

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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Abbott , R., Abbott , T. D., Abraham , S., et al. 2020 b , , 900, L13

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Abbott , R., Abbott , T. D., Acernese , F., et al. 2023, Physical Review X, 13, 041039

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Abbott, R., Abbott, T. D., Acernese, F., et al. 2023, Phys. Rev. X, 13, 011048

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Addari , F., Marigo , P., Bressan , A., et al. 2024, , 964, 51

2024