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The IACOB project XIV. New clues on the location of the TAMS in the massive star domain

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A volume-limited sample of 670 O and B stars places the end of the main sequence at 22.5 kK across luminosities from 4.3 to 5.7.

desk verdict A volume-limited and homogeneous sample finally puts an empirical TAMS at ~22.5 kK across 12-40 Msun, but the quantitative fit needs sensitivity analysis before being adopted. read the letter →

arxiv 2501.17984 v2 pith:6JWGET5Q submitted 2025-01-29 astro-ph.SR astro-ph.GA

A. de Burgos , S. Simón-Díaz , M. A. Urbaneja , G. Holgado , S. Ekström , M. C. Ramírez-Tannus , E. Zari This is my paper · ORCID
classification astro-ph.SRastro-ph.GA
keywords massivestarsterminal-agemainsequenceHertzsprung-RusselldiagramspectroscopicbinariesstellarrotationGaiadistancesO-typebluesupergiants
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

The paper attempts to establish where the main sequence ends for massive stars, a boundary called the terminal-age main sequence (TAMS), using 670 Galactic O- and B-type stars within 2500 parsecs. It claims that star density in the Hertzsprung-Russell diagram (luminosity against surface temperature) drops abruptly below about 22.5 kK, in every luminosity range from about $\log(L/L_\odot)=4.3$ to $5.7$. Two independent tracers reinforce the same boundary: fast-rotating stars nearly disappear on the cool side, and the fraction of single-line spectroscopic binaries falls from 39% to 15% across it. The paper therefore proposes an empirical TAMS line, $\log(L/L_\odot) = 0.47\,T_{\rm eff} - 5.42$ with $T_{\rm eff}$ in kK, and compares it with published evolutionary tracks. This matters because the width of the massive-star main sequence is a long-standing uncertainty in stellar evolution.

What carries the argument

The central object is the volume-limited sample itself: 670 stars within 2500 pc with $B_{\rm mag}<11$, each with effective temperature, surface gravity, projected rotational velocity $v\sin i$, binary status from multi-epoch spectra, and a luminosity derived from astrometric distances. The diagnostic identity is the drop in the cumulative distribution of stars with $T_{\rm eff}$: the TAMS is placed where the CDF has risen by 0.15, and fitting the four luminosity bins yields $\log(L/L_\odot) = 0.47\,T_{\rm eff} - 5.42$ [dex], $T_{\rm eff}$ in kK. Two companion diagnostics carry independent weight: the disappearance of stars with $v\sin i > 100$ km/s near the boundary and the decrease in the SB1 fraction from 39% hot-side to 15% cool-side stars.

What would settle it

Re-count the stars within 2500 pc after including the currently missing B0-type stars and the excluded disk-bearing and double-lined binary populations, assigning each an effective temperature. If adding them fills the hot side and removes the density drop below about 22.5 kK, the boundary is an artifact of sample selection; if the drop survives at the same temperature, the empirical TAMS is confirmed. A related check is to compute the same cumulative distribution for an independent complete sample, such as massive stars in the Magellanic Clouds, where the excluded populations are cataloged separately.

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Extended reading notes

Core claim

The central discovery is empirical: in a volume-limited spectroscopic HR diagram, the number of stars per effective-temperature bin falls sharply near 22.5 kK for all luminosity ranges between $\log(L/L_\odot)=4.3$ and $5.7$, and the same temperature marks the cool edge of fast rotators and the step down in single-lined binary fraction. The paper interprets this boundary as the TAMS, where core hydrogen is exhausted and stars evolve quickly to cooler temperatures. Placing the boundary at the 15% rise of the cumulative temperature distribution gives the linear relation $\log(L/L_\odot) = 0.47\,T_{\rm eff} - 5.42$ [dex]. The boundary is stable when the distance cut changes from 1500 to 4000 pc. Comparing with the three widely used evolutionary model grids, the authors find no single set of models reproduces the empirical TAMS over the full 12–40 $M_\odot$ mass range, and argue that the required adjustment is mostly in the convective overshooting parameter rather than in special physics such as envelope inflation. They also argue that the lack of fast rotators below the boundary is explained by short post-main-sequence timescales and spin-down near critical rotation, not by enhanced mass-loss braking, because newer mass-loss measurements do not show the predicted jump at about 22 kK.

Load-bearing premise

The claim rests on the assumption that the sharp fall in star counts at about 22.5 kK marks the end of core hydrogen burning, rather than being partly produced by selection effects: the sample excludes disk-bearing stars, double-lined binaries, and hypergiants, and is missing a comparatively large number of B0-type stars, and those populations could be concentrated on the hot side of the boundary.

Editorial extensions

If this is right

  • The main sequence for roughly 12–40 $M_\odot$ stars ends at a nearly vertical boundary around 22.5 kK, so blue supergiants sitting cool of this line are mostly post-main-sequence objects rather than a separate main-sequence population.
  • The empirical TAMS gives evolutionary models a new calibration point for convective overshooting: the paper's comparison implies more overshooting for two standard model grids between 15 and 30 $M_\odot$ and less overshooting above 25 $M_\odot$ for the third.
  • The decline of fast rotators beyond the TAMS does not require the bi-stability braking mechanism; statistical scarcity of post-main-sequence stars plus spin-down near critical velocity can account for it.
  • The dominant slowly rotating component of the $v\sin i$ distribution supports low to mild initial rotation, $v_{\rm ini} \lesssim 150$ km/s, for the bulk of massive stars, while the fast-rotating tail is better explained as binary-interaction products.
  • The drop in both SB1 and SB2+ systems across the boundary can be used as an independent empirical tool for locating the TAMS in other samples.

Reading between the lines

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

  • If the completeness of the missing B0-type stars near 28 kK is improved, the density drop could sharpen and shift slightly; the paper itself notes that such stars would probably strengthen the hot side of the boundary, so this is a direct test of the line's exact position.
  • The same volume-limited methodology applied to massive stars in the Magellanic Clouds would test whether the 22.5 kK boundary shifts with metallicity, which the model grids predict at some level.
  • A testable prediction is that the few SB1 systems found cool of the TAMS are mostly systems heading toward the red supergiant phase; measuring their orbital periods and surface abundances could distinguish that channel from blue-loop products.
  • Extending the sample beyond 40 $M_\odot$ would directly test whether envelope inflation is needed at high mass, since the paper's data rule out the previously inferred overdensity of 25–40 $M_\odot$ stars below about 20 kK.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The manuscript presents an updated empirical Hertzsprung-Russell diagram for 876 Galactic O- and B-type stars from the IACOB project, with 670 stars within 2500 pc used as the main volume-limited sample. Spectroscopic parameters are derived with FASTWIND, distances come from Gaia/Bailer-Jones, projected rotational velocities from iacob-broad, and SB1 status from multi-epoch radial velocities. The central result is a drop in stellar density at about 22.5 kK across luminosity ranges log L/Lsun ~ 4.3 to 5.7, interpreted as the terminal-age main sequence and fitted as log(L/Lsun) = 0.47 Teff - 5.42 (Teff in kK). Additional diagnostics—the disappearance of fast rotators and a drop in the SB1 fraction from 39% to 15%—are used to corroborate the location. The empirical TAMS is compared with the evolutionary models of Brott et al. (2011), Ekström et al. (2012), and Choi et al. (2016), and the authors argue that the comparison calls for a revision of the overshooting parameter.

Significance. If the empirical TAMS location is correct, this is a substantial step beyond Castro et al. (2014): the sample is larger, homogeneously analyzed, volume-limited, and combines density, rotation, and binarity diagnostics in one dataset. The completeness evaluation against the ALS III catalog and the use of dedicated thresholds to separate SB1 systems from intrinsic variability are clear strengths, as is the explicit discussion of possible contamination by blue-loop and binary-merger products in Sec. 5.3. The main quantitative claim, however, rests on a cumulative-fraction cutoff chosen by inspection, with no quoted uncertainties or sensitivity tests, and the sample exclusions and missing stars can affect the hot-side counts that set the percentile. These issues are acknowledged in Sec. 4.3 and Appendix A but are not quantified. With robustness tests and a quantitative treatment of completeness biases, the paper would provide strong empirical constraints on the width of the massive-star main sequence.

major comments (4)
  1. [Section 4.1 (Fig. 3) and Eq. (1)] The TAMS anchor points are defined as the effective temperatures at which the cumulative temperature distribution of the retained stars reaches 0.15 in each of four luminosity bins, and the linear fit log(L/Lsun) = 0.47 Teff - 5.42 is based on these four values. As the paper itself states in Sec. 4.3, this definition depends on the number of objects on the hot side of the TAMS, and each CDF is normalized to the stars actually retained. Please add a sensitivity analysis: vary the cumulative threshold (e.g., 0.10 and 0.20), repeat the fit, and report bootstrap or other uncertainties for the four Teff values and for the slope and intercept of the TAMS line. Without this, the quantitative boundary and the quoted analytical form are not established to the precision implied by the text.
  2. [Section 3 and Appendix A] Appendix A shows that B0-type stars, with a mean Teff near 28 kK, constitute the largest group of missing objects, and Sec. 2.1 explains that Be stars, SB2+ systems, and hypergiants are deliberately excluded. The completeness analysis in Sec. 3 quantifies completeness in distance and magnitude, but it does not demonstrate that the missing and excluded populations are distributed neutrally in Teff across the 22-25 kK transition. Because each luminosity-bin CDF is normalized to the retained sample, a deficit of hot-side objects will shift the 0.15 percentile to cooler temperatures. Please quantify this effect, for example by assigning representative parameters to the missing ALS III stars and recomputing the CDFs, or by deriving an upper bound on the shift. The qualitative statement that missing B0 stars would 'probably strengthen the position of the TAMS' is not sufficient support for a quantitative claim.
  3. [Section 4.4 and Appendix D] The drop in the SB1 fraction from 39% on the hot side (30-22.5 kK) to 15% on the cool side (22.5-15 kK) is presented as an independent confirmation of the TAMS location. However, the RVpp detection thresholds in Appendix D depend on Teff and luminosity, and the text notes a higher detection threshold at high luminosities without assessing whether the cool-side stars are systematically harder to classify as SB1. If detection completeness varies across the boundary, part of the apparent 39% to 15% drop could be a selection effect. Please provide a detection-completeness correction, or at least bound the maximal selection effect, before using the SB1 drop as a corroborating diagnostic.
  4. [Section 4.1 and Fig. 3] The claimed consistency of the density drop across the 1500, 2500, and 4000 pc cuts is not uniform: for stars with log(L/Lsun) > 5.35 at 4000 pc the drop is shifted toward cooler temperatures, and for the 1500 pc high-luminosity bin the authors state that the sample is too small to show the drop. Since the cross-distance agreement is used as evidence of robustness, please report significance levels for the density drop in each luminosity bin and distance cut (e.g., comparing counts within a few kK of the adopted boundary) and provide uncertainties for the four TAMS anchor points. This would place the fitted TAMS relation on a firmer statistical basis.
minor comments (4)
  1. [Throughout] The text consistently renders the projected rotational velocity as '3 sin i'; this should be 'v sin i' in the published version.
  2. [Section 6 and Table 1] The Conclusions state a completeness of about 60% for stars within 2500 pc and Bmag < 11, whereas Table 1 lists 77% at 2 kpc and 62% at 3 kpc; please specify the exact value at 2500 pc and clarify whether observed-but-unanalyzed stars are included in the completeness estimate.
  3. [Figure 3 caption] The CDFs in the bottom row of Fig. 3 are central to the TAMS definition, but the caption does not specify the histogram bin width or the exact luminosity ranges; please provide these details.
  4. [Section 4.3] The FR-TAMS polynomial log(L/Lsun) = -0.001 Teff^2 + 0.154 Teff + 1.71 is quoted without uncertainties, and the SR-TAMS is quoted as Teff = 22.65 +/- 0.11 kK without a description of how the 0.11 kK uncertainty was derived; please add the error analysis for both quantities.

Circularity Check

0 steps flagged · score 2.0 of 10

Empirical TAMS measurement is largely self-contained; minor self-cited thresholds for the rotation and SB1 diagnostics are not load-bearing for the central claim.

full rationale

The central quantitative claim (empirical TAMS at about 22.5 kK, with the linear form log(L/Lsun) = 0.47 Teff - 5.42) is an observed density drop located by a CDF = 0.15 quantile of the effective-temperature histogram in each luminosity bin. It is not derived from the rotation or binarity data, and no parameter is fitted to those data and then renamed a prediction. The v sin i threshold (100 km/s) and the SB1 RVpp thresholds are imported from IACOB companion works with overlapping authorship (de Burgos et al. 2024b; Simon-Diaz et al. subm.), so the rotation-drop and SB1-drop diagnostics are partly self-citation-dependent; however, these support only the secondary evidence and are not the basis for the TAMS position, which is set by the star-count histogram and compared with external benchmarks (Castro et al. 2014, evolutionary tracks, Dunstall et al. 2015). The expected-count exercise in Sect. 5.1.1 combines the same sample's density ratio and fast-rotator fraction, making it an internal consistency check rather than a fully independent prediction, but the resulting count of six versus two observed fast rotators is not forced by construction. The paper's own caveats (dependence of the 0.15-CDF definition on hot-side counts, missing B0 stars strengthening the drop, and additional faint stars shifting it) are robustness and selection-effect limitations, not circularity. Overall, no load-bearing circular step is identified.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central TAMS location rests on observational assumptions about model atmospheres, Gaia distances, ALS III completeness, and SB1 thresholds, and on the interpretive assumption that the density drop marks core hydrogen exhaustion. No new physical entities are introduced. The main free choices are the CDF threshold, the v sin i = 100 km/s split, and the bin and luminosity-range definitions; all are transparent but not independently calibrated.

free parameters (5)
  • CDF threshold for the TAMS drop = 0.15
    Chosen by inspection in Fig. 3 as the cumulative fraction increase that defines the drop in each luminosity range; the resulting Teff values set the empirical TAMS in Sect. 4.1.
  • v sin i fast/slow classification threshold = 100 km/s
    Adopted from de Burgos et al. 2024b to split the two spin-rate components; used throughout to define fast-rotating stars and the FR/SR-TAMS variants in Sect. 4.2.
  • Effective temperature bins for rotation medians = 4 kK width
    Bins used for median and percentile estimates in Fig. 4; the binning choice affects the apparent evolutionary trend of v sin i.
  • Luminosity ranges for TAMS evaluation = log L/Lsun = 4.30-4.65, 4.65-5.00, 5.00-5.35, 5.35-5.70
    The four bins define the histograms and the four TAMS temperature points; results are binned over these intervals in Fig. 3.
  • TAMS linear fit coefficients = log(L/Lsun) = 0.47 Teff - 5.42 dex with Teff in kK
    Linear fit to the four adopted drop temperatures; used to draw the purple TAMS line in Fig. 2.
assumptions (6)
  • domain assumption FASTWIND unclumped model atmospheres give reliable Teff and log g for O9 to B6 stars.
    All spectroscopic parameters used to place stars in the HR diagram come from a FASTWIND grid with MCMC inference (Sect. 2.3); systematic errors in the grid would shift every star and the TAMS.
  • domain assumption Gaia and Bailer-Jones distances with sigma_pi/pi <= 0.15 are unbiased for this sample.
    Luminosities and HR positions rely on these distances (Sect. 2.2); distance errors propagate to log L and affect the TAMS placement.
  • domain assumption The ALS III catalog is a complete reference census of the relevant O/B stars with Bmag < 11 within 4 kpc.
    Completeness percentages and the 2500 pc volume-limited choice are measured against ALS III (Sect. 3); if ALS III is incomplete near the TAMS, the density drop may be spurious.
  • domain assumption The observed drop in stellar density as a function of Teff primarily traces stars leaving the main sequence rather than selection effects or other evolutionary channels.
    This is the interpretive step linking the histogram drop to the TAMS (Sect. 4.1); blue loops, binary mergers, and missing SB2/Be stars are acknowledged as possible contaminants in Sect. 5.3.
  • domain assumption The RVpp thresholds used to identify SB1 systems are correct.
    SB1 classification and the 39% to 15% drop rely on thresholds from Simon-Diaz et al. (submitted), described only in Appendix D.
  • domain assumption Model tracks and the Langer 1998 critical-velocity prescription can be compared directly to the empirical TAMS.
    MIST, Brott, Ekstrom, and Choi tracks and the vcrit lines are used in Sects. 4.2 and 4.3; this assumes the model masses, metallicities, and rotation treatments are representative of the observed sample.

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Pith. "Pith review of The IACOB project XIV. New clues on the location of the TAMS in the massive star domain." pith.science (2026). https://pith.science/paper/6JWGET5Q

@misc{pith2026250117984,
  author       = {Pith},
  title        = {Pith review of: The IACOB project XIV. New clues on the location of the TAMS in the massive star domain},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6JWGET5Q}},
  note         = {Machine review of arXiv:2501.17984}
}
abstract

Massive stars play a very important role in many astrophysical fields. Yet, some fundamental aspects of their evolution remain poorly constrained. In this regard, there is an open debate on the width of the main-sequence (MS) phase. We aim to create an updated Hertzsprung-Russell (HR) diagram that includes a volume-limited and statistically significant sample of massive stars. Our goal is to use this sample to investigate the extension of the MS, including information about projected rotational velocities ($v\sin i$) and the spectroscopic binary status. We combine spectroscopic parameters derived with FASTWIND stellar atmosphere code and Gaia distances to obtain stellar parameters for 876 Galactic luminous O- and B-type stars gathered within the IACOB project. We use the ${\tt iacob-broad}$ tool to derive $v\sin i$ estimates and multi-epoch spectra to identify single/double-line spectroscopic binaries (SB1/SB2). We present an HR diagram for 670 stars located within 2500pc balancing completeness and number. We evaluate the extension of the MS in terms of the drop in the relative number of stars as a function of effective temperature ($T_{\rm eff}$). We find a consistent boundary at $\approx$22.5kK within the full range of luminosities that we use to delineate the terminal-age main sequence (TAMS). We obtain a smooth decrease of the highest $v\sin i$ with $T_{\rm eff}$ along the MS, likely limited by the critical velocity. We consider this effect combined with a lower expected fraction of stars beyond the MS as the best explanation for the lack of fast-rotating objects in the post-MS region. Our results favor low to mild initial rotation for the full sample and a binary past for the tail of fast-rotating stars. The prominence of SB1/SB2 systems in the MS, and the 25% decrease in the relative fraction of SB1 systems when crossing the TAMS can further delineate its location.

Figures

Figures reproduced from arXiv: 2501.17984 by the authors.

Figure 1
Figure 1. Gaia CMD including the stars in the sample and other missing stars included in the ALS III catalog (Pantaleoni González, et al., in prep.). All the stars have Bmag < 11 and distances below 4 kpc. The two diagonal dashed black lines mark the reddening line of a 20 M⊙ star at the zero-age MS (ZAMS, bottom) and at 30 kK (top). Both are extended up to a ∆(Av) = 2. Stars shown in green include those for which both the us… view at source ↗
Figure 2
Figure 2. Hertzsprung-Russell diagrams showing the stars in our sample. From left to right, each panel limits the sample to stars within 1500 (221 stars), 2500 (670 stars), and 4000 pc (852 stars) of distance, respectively. The stars with 3sin i > 100 km s−1 are indicated with cyan circles, whereas the rest are shown in orange. The average uncertainties are indicated with error bars in the lower-left corner of the panels. Eac… view at source ↗
Figure 3
Figure 3. Number of stars with respect to their effective temperature. The histograms in the top four rows of subpanels separate stars within the indicated range of luminosities using different colors. Cyan bins indicate fast-rotating stars with 3sin i > 100 km s−1 . Each histogram displays the total number of stars and of fast-rotating objects (FR). Each column separate stars by their distances, as indicated in the top panel… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Hertzsprung-Russell diagrams showing different evolutionary tracks for solar metallicity together with different predictions for the lo￾cation of the TAMS as indicated in each legend. The top panel includes tracks with no initial rotation, and in the bottom panel the t…
Figure 6
Figure 6. Figure 6: Similar HR diagram as in [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Histograms of the number of spectroscopic binaries against spec￾tral type or log10(Teff), limited to a distance of 2500 pc. The top panel include SB2+ systems for which the spectral type is taken from the pri￾mary star (see also Sect. 5.2 for further details). The midd…

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