Diffusion-inclusive late-hot-flasher evolution models and complete abundance patterns for the helium-rich extreme horizontal branch (blue hook) stars of ω Centauri

A homogeneous non-local thermodynamic equilibrium (NLTE) spectroscopic analysis of 38 extreme horizontal branch (EHB) stars in the globular cluster ω Centauri found that the 25 helium-rich subdwarfs cluster at effective temperatures of 35,000–40,000 K, that their atmospheric carbon and helium abundances obey a tight positive correlation in the log N(C)/N(H)–log N(He)/N(H) plane, and that existing late-hot-flasher evolutionary tracks predict systematically higher surface gravities than measured (Latour et al. 2014, ApJ 795, 106). Because unimpeded gravitational settling would transform an initially helium- and carbon-rich atmosphere into a hydrogen-dominated one within roughly $10^3$ yr — far shorter than EHB evolutionary timescales — the observed abundances can only persist if settling is counteracted, most plausibly by weak stellar winds or turbulence. The open problem is a quantitative physical account of this population: evolutionary calculations for late hot flashers that include gravitational settling, radiative levitation, and plausible weak-wind or turbulence prescriptions calibrated to ω Centauri, reproducing the observed positions in the $\log g$–$T_{\rm eff}$ plane and the time-dependent surface abundances; identification and quantification of the settling-inhibiting mechanism; higher-resolution spectroscopy securing nitrogen and oxygen abundances; and a quantitative explanation of the differences between the cluster He-rich subdwarfs and the hotter, more massive field He-sdO stars. Follow-up work has confirmed the cluster–field dichotomy, revealed an unexplained low spectroscopic-mass problem in ω Cen, and established a merger origin for field He-sdO stars, but as of 2026 no late-hot-flasher tracks including diffusion have been published and the core problem remains open.

Background

Horizontal branch (HB) stars are low-mass stars burning helium in their cores after having lost most of their hydrogen envelopes on the red giant branch; in the most extreme stripping regime they form the extreme horizontal branch (EHB), observed optically as compact hot subdwarf B (sdB) and subdwarf O (sdO) stars with effective temperatures $T_{\rm eff}$ above roughly 20,000 K and surface gravities $\log g$ of about 5–6.5 (cgs). The zero-age and terminal-age HB (ZAHB, TAHB) mark the beginning and end of core-helium burning. Several massive globular clusters, most prominently ω Centauri — a massive, chemically inhomogeneous cluster hosting helium-enriched 'second-generation' stellar populations with initial helium mass fraction up to $Y\sim0.4$ — show a 'blue hook': a hook-shaped extension of the HB to hotter, ultraviolet-brighter magnitudes occupied by helium-rich EHB stars. Two origins are debated for these He-rich stars: (i) He-enhanced second-generation progenitors, which should show no anomalous heavy-element enrichment, and (ii) the 'late hot flasher' channel, in which a red giant loses its envelope so early that the degenerate helium core ignites while descending or already on the white-dwarf cooling track; convective mixing driven by this flash can then dredge up hydrogen and, in the 'deep mixing' case, burn it, leaving an atmosphere predicted to be about 96% helium and 3–4% carbon by mass, while 'shallow mixing' leaves more hydrogen and less carbon. The reference late-hot-flasher calculations are those of Miller Bertolami et al. (2008, A&A 491, 253, and tracks at Z=0.001 therein); their standard tracks do not include atmospheric diffusion, and the paper's own exploratory calculations already showed that unimpeded element diffusion can transform post-hot-flasher He-rich atmospheres into He-deficient ones. Spectroscopic tests in ω Cen began with Moehler et al. (2002, A&A 395, 37), and analogous blue hook populations exist in NGC 2808 (Moehler et al. 2004); moderately high resolution spectroscopy of hot horizontal-branch stars in ω Cen (Moehler et al. 2011) likewise found that the blue hook stars contain much less helium than the deep-mixing predictions and that the predicted carbon and nitrogen enrichment could not be verified at that stage. Field comparison samples of helium-rich subdwarf O (He-sdO) stars were built by Stroeer et al. (2007) and Németh et al. (2012), and the hot-subdwarf review of Heber (2009) documents the cluster–field difference. In this context, Latour et al. (2014, ApJ 795, 106) obtained 2.6 Å resolution FORS2/VLT spectra of 38 ω Cen EHB stars and analyzed them homogeneously with NLTE, metal line-blanketed TLUSTY/SYNSPEC model atmospheres (non-local thermodynamic equilibrium accounts for the strong departure of the level populations of these hot, low-density atmospheres from thermodynamic equilibrium; 'metal line blanketing' is the blocking of outgoing radiation by huge numbers of metal lines). They found three groups: 7 H-rich sdB stars below ~35,000 K, 25 He-rich subdwarfs (log N(He)/N(H) above about −1) at 35,000–40,000 K, and 6 hotter H-rich sdO stars around and above ~45,000 K; they measured carbon abundances for 30 stars and found the relation log N(C)/N(H) = 1.36(±0.039) log N(He)/N(H) − 2.56(±0.027), with carbon mass fractions up to about 1.5% — far below the 3–4% predicted for deep mixing, and with only three stars reaching more than 90% helium by mass. Two facts make the problem sharp. First, atomic diffusion — gravitational settling of heavier species balanced against radiative levitation (radiation pressure selectively supporting particular ions) — should operate in these hot, radiative atmospheres: unimpeded settling would convert an initially He- and C-rich atmosphere into a hydrogen-dominated one within only $\sim10^3$ yr, orders of magnitude shorter than EHB evolution, so a competing agent (weak winds or turbulence) must inhibit it. Second, the late-hot-flasher tracks of Miller Bertolami et al. (2008) do not reproduce the measured positions of the He-rich stars in the $\log g$–$T_{\rm eff}$ plane, predicting systematically higher surface gravities than measured. The nitrogen and oxygen abundances needed to discriminate formation channels remain unmeasured at this resolution: N lines are only discernible in the most helium-rich stars, and the oxygen abundance had to be reduced to about one-tenth solar for 18 stars to avoid O II blends mimicking weak C III lines.

Problem Statement

Deliver a quantitative physical account of the helium-rich extreme horizontal branch (blue hook) population of the globular cluster ω Centauri, consisting of the following linked questions sharing one objective. (1) Evolutionary calculations for late hot flashers at ω Centauri metallicities that incorporate gravitational settling, radiative levitation, and physically motivated prescriptions for weak stellar winds and/or turbulence, and that (a) reproduce the measured positions of the He-rich stars in the $\log g$–$T_{\rm eff}$ plane, where current diffusion-free tracks predict systematically higher surface gravities than observed, and (b) predict time-dependent surface compositions consistent with the measured helium and carbon abundances, including the observed relation log N(C)/N(H) = 1.36(±0.039) log N(He)/N(H) − 2.56(±0.027) and the fact that carbon mass fractions reach only about 1.5% and only a few stars exceed 90% helium by mass, against the roughly 96% He and 3–4% C predicted for deep mixing. The same calculations should clarify the spectroscopic-mass problem of this population (spectroscopic masses — derived from the measured atmospheric parameters together with photometry and the cluster distance — average about 0.38 solar masses, versus roughly 0.5 solar masses expected from stellar evolution). (2) The identification and quantification of the mechanism(s) that inhibit gravitational settling in these atmospheres — their nature (weak wind versus turbulence or other), strength (mass-loss rates or effective diffusivities), and parameter dependence — consistent with the survival of helium- and carbon-rich atmospheres over EHB lifetimes and with the observed abundance patterns. (3) Firm nitrogen and oxygen abundance determinations for the ω Cen He-rich EHB sample, removing the current reliance on reduced-oxygen assumptions and marginal nitrogen detections, so that the full abundance pattern can discriminate between formation channels. Establish quantitatively which of these N and O values the existing and archival spectra can and cannot constrain; for the values the data cannot yield, determine and state the higher-resolution, higher-signal-to-noise observations that would be required to obtain them. (4) A quantitative physical explanation of the systematic differences between the cluster He-rich subdwarfs ($T_{\rm eff}\approx35{,}000$–$40{,}000$ K) and the hotter, more massive field He-sdO population (~45,000 K): progenitor age and metallicity, selection effects, or different formation-channel efficiencies in different environments. The single overarching objective is a coupled theory-plus-observation account in which diffusion-inclusive late-hot-flasher evolution calibrated to ω Centauri explains the observed atmospheric parameters, the helium–carbon abundance relation, the population's spectroscopic masses, and its distinctness from the field He-sdO population. The question is not restricted to any particular numerical method, code, or answer form.

References

1. Latour, M., Randall, S. K., Fontaine, G., Bono, G., Calamida, A., & Brassard, P. 2014, 'A Helium-Carbon Correlation on the Extreme Horizontal Branch in ω Centauri', The Astrophysical Journal 795, 106. DOI: 10.1088/0004-637X/795/2/106. URL: https://doi.org/10.1088/0004-637X/795/2/106 (arXiv:1409.4042).
2. Miller Bertolami, M. M., Althaus, L. G., Unglaub, K., & Weiss, A. 2008, 'Modeling He-rich subdwarfs through the hot-flasher scenario', Astronomy & Astrophysics 491, 253. DOI: 10.1051/0004-6361:200810373. URL: https://doi.org/10.1051/0004-6361:200810373 (arXiv:0808.3580).
3. Moehler, S., Sweigart, A. V., Landsman, W. B., & Dreizler, S. 2002, 'Spectroscopic analyses of the "blue hook" stars in ω Centauri: A test of the late hot flasher scenario', Astronomy & Astrophysics 395, 37. DOI: 10.1051/0004-6361:20021248. URL: https://doi.org/10.1051/0004-6361:20021248.
4. Moehler, S., Sweigart, A. V., Landsman, W. B., Hammer, N. J., & Dreizler, S. 2004, 'Spectroscopic analyses of the blue hook stars in NGC 2808: A more stringent test of the late hot flasher scenario', Astronomy & Astrophysics 415, 313. DOI: 10.1051/0004-6361:20034505. URL: https://doi.org/10.1051/0004-6361:20034505.
5. Moehler, S., Dreizler, S., Lanz, T., Bono, G., Sweigart, A. V., Calamida, A., & Nonino, M. 2011, 'The hot horizontal-branch stars in ω Centauri', Astronomy & Astrophysics 526, A136. DOI: 10.1051/0004-6361:201015020. URL: https://doi.org/10.1051/0004-6361:201015020 (arXiv:1009.3191).
6. Stroeer, A., Heber, U., Lisker, T., Napiwotzki, R., Dreizler, S., Christlieb, N., & Reimers, D. 2007, 'Hot subdwarfs from the ESO supernova Ia progenitor survey — II. Atmospheric parameters of subdwarf O stars', Astronomy & Astrophysics 462, 269. DOI: 10.1051/0004-6361:20065564. URL: https://doi.org/10.1051/0004-6361:20065564.
7. Németh, P., Kawka, A., & Vennes, S. 2012, 'A selection of hot subluminous stars in the GALEX survey — II. Subdwarf atmospheric parameters', Monthly Notices of the Royal Astronomical Society 427, 2180. DOI: 10.1111/j.1365-2966.2012.22009.x. URL: https://doi.org/10.1111/j.1365-2966.2012.22009.x.
8. Heber, U. 2009, 'Hot subdwarf stars', Annual Review of Astronomy and Astrophysics 47, 211. DOI: 10.1146/annurev-astro-082708-101836. URL: https://doi.org/10.1146/annurev-astro-082708-101836.
9. Latour, M., Randall, S. K., Calamida, A., Geier, S., & Moehler, S. 2018, 'SHOTGLAS. I. The ultimate spectroscopic census of extreme horizontal branch stars in ω Centauri', Astronomy & Astrophysics 618, A15. DOI: 10.1051/0004-6361/201833129. URL: https://doi.org/10.1051/0004-6361/201833129 (arXiv:1806.09436).
10. Tailo, M., D'Antona, F., Vesperini, E., Di Criscienzo, M., Ventura, P., Milone, A. P., Bellini, A., Dotter, A., Decressin, T., D'Ercole, A., Caloi, V., & Capuzzo-Dolcetta, R. 2015, 'Rapidly rotating second-generation progenitors for the "blue hook" stars of ω Centauri', Nature 523, 318. DOI: 10.1038/nature14516. URL: https://doi.org/10.1038/nature14516.
11. Lei, Z., Chen, X., Zhang, F., & Han, Z. 2015, 'A possible formation channel for blue hook stars in globular clusters', Monthly Notices of the Royal Astronomical Society 449, 2741. DOI: 10.1093/mnras/stv544. URL: https://doi.org/10.1093/mnras/stv544 (arXiv:1503.08885).
12. Lei, Z., Zhao, G., Zeng, A., Shen, L., Lan, Z., Jiang, D., & Han, Z. 2016, 'A possible formation channel for blue hook stars in globular cluster — II. Effects of metallicity, mass ratio, tidal enhancement efficiency and helium abundance', Monthly Notices of the Royal Astronomical Society 463, 3449. DOI: 10.1093/mnras/stw2242. URL: https://doi.org/10.1093/mnras/stw2242.
13. Latour, M., Randall, S. K., Chayer, P., Fontaine, G., Calamida, A., Ely, J., Brown, T. M., & Landsman, W. 2017, 'Just how hot are the ω Centauri extreme horizontal branch pulsators?', Astronomy & Astrophysics 600, A130. DOI: 10.1051/0004-6361/201630132. URL: https://doi.org/10.1051/0004-6361/201630132.
14. Randall, S. K., Calamida, A., Fontaine, G., Monelli, M., Bono, G., Alonso, M. L., Van Grootel, V., Brassard, P., Chayer, P., Catelan, M., Littlefair, S., Dhillon, V. S., & Marsh, T. R. 2016, 'Pulsating hot O subdwarfs in ω Centauri: mapping a unique instability strip on the extreme horizontal branch', Astronomy & Astrophysics 589, A1. DOI: 10.1051/0004-6361/201528006. URL: https://doi.org/10.1051/0004-6361/201528006.
15. Latour, M., Hämmerich, S., Dorsch, M., Heber, U., Husser, T.-O., Kamann, S., Dreizler, S., & Brinchmann, J. 2023, 'SHOTGLAS. II. MUSE spectroscopy of blue horizontal branch stars in the core of ω Centauri and NGC 6752', Astronomy & Astrophysics 677, A86. DOI: 10.1051/0004-6361/202346597. URL: https://doi.org/10.1051/0004-6361/202346597 (arXiv:2306.14549).
16. Latour, M., Green, E. M., Dorsch, M., Van Grootel, V., Chayer, P., Charpinet, S., Heber, U., Randall, S. K., & Ma, X.-Y. 2026, 'The Arizona-Montréal Spectroscopic Survey of hot subluminous stars', Astronomy & Astrophysics 705, A248. DOI: 10.1051/0004-6361/202557314. URL: https://doi.org/10.1051/0004-6361/202557314 (arXiv:2511.02539).
17. Miller Bertolami, M. M., Battich, T., Córsico, A. H., Althaus, L. G., & Wachlin, F. C. 2022, 'An evolutionary channel for CO-rich and pulsating He-rich subdwarfs', Monthly Notices of the Royal Astronomical Society: Letters 511, L60. DOI: 10.1093/mnrasl/slab134. URL: https://doi.org/10.1093/mnrasl/slab134 (arXiv:2202.05635).
18. Battich, T., Miller Bertolami, M. M., Weiss, A., Dorsch, M., Serenelli, A. M., & Justham, S. 2025, 'The i-processes nucleosynthesis during the formation of He-rich hot-subdwarf stars', Astronomy & Astrophysics 699, A298. DOI: 10.1051/0004-6361/202453572. URL: https://doi.org/10.1051/0004-6361/202453572.
19. Byrne, C. M., Jeffery, C. S., Tout, C. A., & Hu, H. 2018, 'The effects of diffusion in hot subdwarf progenitors from the common envelope channel', Monthly Notices of the Royal Astronomical Society 475, 4728. DOI: 10.1093/mnras/sty158. URL: https://doi.org/10.1093/mnras/sty158.
20. Geier, S., Reindl, N., Dorsch, M., Jadhav, V., Todt, H., Werner, K., Heber, U., Miller Bertolami, M. M., Battich, T., & Filiz, S. 2026, 'Studying hot evolved stars with ultraviolet spectroscopy', arXiv:2606.11367. URL: https://arxiv.org/abs/2606.11367.
21. Arancibia-Rojas, E., Zorotovic, M., Vučković, M., Bobrick, A., & Durán-Reyes, A. 2026, 'Shaping the horizontal branch: the role of envelope mass in the evolution of stripped core-helium-burning stars', arXiv:2606.12242. URL: https://arxiv.org/abs/2606.12242.