Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Carbon star formation as seen through the non-monotonic initial–final mass relation

This article has been updated

Abstract

The initial–final mass relation (IFMR) links the birth mass of a star to the mass of the compact remnant left at its death. While the relevance of the IFMR across astrophysics is universally acknowledged, not all of its fine details have yet been resolved. A new analysis of a few carbon–oxygen white dwarfs in old open clusters of the Milky Way led us to identify a kink in the IFMR, located over a range of initial masses, 1.65 Mi/M 2.10. The kink’s peak in white dwarf mass of about 0.70−0.75 M is produced by stars with Mi ≈ 1.8−1.9 M, corresponding to ages of about 1.8−1.7 Gyr. Interestingly, this peak coincides with the initial mass limit between low-mass stars that develop a degenerate helium core after central hydrogen exhaustion, and intermediate-mass stars that avoid electron degeneracy. We interpret the IFMR kink as the signature of carbon star formation in the Milky Way. This finding is critical to constraining the evolution and chemical enrichment of low-mass stars, and their impact on the spectrophotometric properties of galaxies.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: The semi-empirical IFMR.
Fig. 2: Evolution of the mass-loss rate during the whole TP-AGB evolution of a star with Mi = 1.8 M and solar metallicity.
Fig. 3: Map of the condensation factor, fc, as a function of mass-loss rate and photospheric C/O.
Fig. 4: Calibration of the 3DU efficiency and the resulting theoretical IFMR.
Fig. 5: Integrated energy output emitted from the carbon-star phase.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Montreal WD cooling models are publicly available from http://www.astro.umontreal.ca/~bergeron/CoolingModels. The pulsation periods are computed with fitting relations based on publicly available models that can be found at http://starkey.astro.unipd.it/pulsation_models.html.

Code availability

The stellar evolution codes PARSEC and COLIBRI are not publicly available. The mass-loss routine for carbon stars can be found at https://www.astro.uu.se/coolstars/TOOLS/MLR-routines/C/. The code to compute the dust-grain growth in the outflows of AGB stars can be retrieved from http://www.ita.uni-heidelberg.de/~gail/agbdust/agbdust.html. The code used here to calculate photometry-based WD parameters is available from https://github.com/SihaoCheng/WD_models.

Change history

  • 14 July 2020

    In the version of this Article originally published, the Montreal WD cooling model link in the Data availability statement and the AGB stars link in the Code availability statement were incorrect. They have now been updated.

References

  1. Cescutti, G., Matteucci, F., McWilliam, A. & Chiappini, C. The evolution of carbon and oxygen in the bulge and disk of the Milky Way. Astron. Astrophys. 505, 605–612 (2009).

    ADS  Google Scholar 

  2. Gustafsson, B., Karlsson, T., Olsson, E., Edvardsson, B. & Ryde, N. The origin of carbon, investigated by spectral analysis of solar-type stars in the Galactic Disk. Astron. Astrophys. 342, 426–439 (1999).

    ADS  Google Scholar 

  3. Mattsson, L. The origin of carbon: low-mass stars and an evolving, initially top-heavy IMF? Astron. Astrophys. 515, A68 (2010).

    ADS  Google Scholar 

  4. Bensby, T. & Feltzing, S. The origin and chemical evolution of carbon in the galactic thin and thick discs. Mon. Not. R. Astron. Soc. 367, 1181–1193 (2006).

    ADS  Google Scholar 

  5. Karakas, A. I. & Lattanzio, J. C. The Dawes Review 2: nucleosynthesis and stellar yields of low- and intermediate-mass single stars. Publ. Astron. Soc. Aus. 31, e030 (2014).

    ADS  Google Scholar 

  6. Herwig, F. Evolution of asymptotic giant branch stars. Annu. Rev. Astron. Astrophys. 43, 435–479 (2005).

    ADS  Google Scholar 

  7. Salaris, M., Serenelli, A., Weiss, A. & Miller Bertolami, M. Semi-empirical white dwarf initial–final mass relationships: a thorough analysis of systematic uncertainties due to stellar evolution models. Astrophys. J. 692, 1013–1032 (2009).

    ADS  Google Scholar 

  8. Kalirai, J. S., Marigo, P. & Tremblay, P.-E. The core mass growth and stellar lifetime of thermally pulsing asymptotic giant branch stars. Astrophys. J. 782, 17 (2014).

    ADS  Google Scholar 

  9. Bird, J. C. & Pinsonneault, M. H. A bound on the light emitted during the thermally pulsing asymptotic giant branch phase. Astrophys. J. 733, 81 (2011).

    ADS  Google Scholar 

  10. Marigo, P. & Girardi, L. Coupling emitted light and chemical yields from stars: a basic constraint to population synthesis models of galaxies. Astron. Astrophys. 377, 132–147 (2001).

    ADS  Google Scholar 

  11. Weidemann, V. Revision of the initial-to-final mass relation. Astron. Astrophys. 363, 647–656 (2000).

    ADS  Google Scholar 

  12. Kalirai, J. S. et al. The initial–final mass relation: direct constraints at the low-mass end. Astrophys. J. 676, 594–609 (2008).

    ADS  Google Scholar 

  13. Cummings, J. D., Kalirai, J. S., Tremblay, P.-E. & Ramirez-Ruiz, E. Two massive white dwarfs from NGC 2323 and the initial–final mass relation for progenitors of 4 to 6.5 M. Astrophys. J. 818, 84 (2016).

    ADS  Google Scholar 

  14. Kalirai, J. S. et al. The masses of population II white dwarfs. Astrophys. J. 705, 408–425 (2009).

    ADS  Google Scholar 

  15. Cummings, J. D., Kalirai, J. S., Tremblay, P.-E., Ramirez-Ruiz, E. & Choi, J. The white dwarf initial–final mass relation for progenitor stars from 0.85 to 7.5 M. Astrophys. J. 866, 21 (2018).

    ADS  Google Scholar 

  16. Williams, K. A. et al. Ensemble properties of the white dwarf population of the old, solar metallicity open star cluster Messier 67. Astrophys. J. 867, 62 (2018).

    ADS  Google Scholar 

  17. Canton, P. The Initial–Final Mass Relation Revisited: A Monte Carlo Approach with the Addition of the M67 White Dwarf Population. PhD thesis, Univ. Oklahoma (2018).

  18. Tremblay, P.-E. et al. The field white dwarf mass distribution. Mon. Not. R. Astron. Soc. 461, 2100–2114 (2016).

    ADS  Google Scholar 

  19. El-Badry, K., Rix, H.-W. & Weisz, D. R. An empirical measurement of the initial–final mass relation with Gaia white dwarfs. Astrophys. J. Lett. 860, L17 (2018).

    ADS  Google Scholar 

  20. Bladh, S., Eriksson, K., Marigo, P., Liljegren, S. & Aringer, B. Carbon star wind models at solar and sub-solar metallicities: a comparative study. I. Mass loss and the properties of dust-driven winds. Astron. Astrophys. 623, A119 (2019).

    ADS  Google Scholar 

  21. Eriksson, K., Nowotny, W., Höfner, S., Aringer, B. & Wachter, A. Synthetic photometry for carbon-rich giants. IV. An extensive grid of dynamic atmosphere and wind models. Astron. Astrophys. 566, A95 (2014).

    ADS  Google Scholar 

  22. Mattsson, L., Wahlin, R. & Höfner, S. Dust driven mass loss from carbon stars as a function of stellar parameters. I. A grid of solar-metallicity wind models. Astron. Astrophys. 509, A14 (2010).

    ADS  Google Scholar 

  23. Marigo, P. & Aringer, B. Low-temperature gas opacity. ÆSOPUS: a versatile and quick computational tool. Astron. Astrophys. 508, 1539–1569 (2009).

    ADS  Google Scholar 

  24. Ferrarotti, A. S. & Gail, H. P. Mineral formation in stellar winds. III. Dust formation in S stars. Astron. Astrophys. 382, 256–281 (2002).

    ADS  Google Scholar 

  25. Ferrarotti, A. S. & Gail, H.-P. Composition and quantities of dust produced by AGB-stars and returned to the interstellar medium. Astron. Astrophys. 447, 553–576 (2006).

    ADS  Google Scholar 

  26. Dell’Agli, F. et al. Asymptotic giant branch and super-asymptotic giant branch stars: modelling dust production at solar metallicity. Mon. Not. R. Astron. Soc. 467, 4431–4440 (2017).

    ADS  Google Scholar 

  27. Nanni, A., Bressan, A., Marigo, P. & Girardi, L. Evolution of thermally pulsing asymptotic giant branch stars—II. Dust production at varying metallicity. Mon. Not. R. Astron. Soc. 434, 2390–2417 (2013).

    ADS  Google Scholar 

  28. Höfner, S. & Olofsson, H. Mass loss of stars on the asymptotic giant branch. Mechanisms, models and measurements. Astron. Astrophys. Rev. 26, 1 (2018).

    ADS  Google Scholar 

  29. Schöier, F. L. & Olofsson, H. Models of circumstellar molecular radio line emission. Mass loss rates for a sample of bright carbon stars. Astron. Astrophys. 368, 969–993 (2001).

    ADS  Google Scholar 

  30. McDonald, I., De Beck, E., Zijlstra, A. A. & Lagadec, E. Pulsation-triggered dust production by asymptotic giant branch stars. Mon. Not. R. Astron. Soc. 481, 4984–4999 (2018).

    ADS  Google Scholar 

  31. McDonald, I. & Trabucchi, M. The onset of the AGB wind tied to a transition between sequences in the period-luminosity diagram. Mon. Not. R. Astron. Soc. 484, 4678–4682 (2019).

    ADS  Google Scholar 

  32. Winters, J. M., Le Bertre, T., Jeong, K. S., Helling, C. & Sedlmayr, E. A systematic investigation of the mass loss mechanism in dust forming long-period variable stars. Astron. Astrophys. 361, 641–659 (2000).

    ADS  Google Scholar 

  33. Cummings, J. D. et al. A novel approach to constrain rotational mixing and convective-core overshoot in stars using the initial–final mass relation. Astrophys. J. 871, L18 (2019).

    ADS  Google Scholar 

  34. Marigo, P., Bressan, A., Nanni, A., Girardi, L. & Pumo, M. L. Evolution of thermally pulsing asymptotic giant branch stars—I. The COLIBRI code. Mon. Not. R. Astron. Soc. 434, 488–526 (2013).

    ADS  Google Scholar 

  35. Wagenhuber, J. & Groenewegen, M. A. T. New input data for synthetic AGB evolution. Astron. Astrophys. 340, 183–195 (1998).

    ADS  Google Scholar 

  36. Ventura, P., Karakas, A., Dell’Agli, F., García-Hernández, D. A. & Guzman-Ramirez, L. Gas and dust from solar metallicity AGB stars. Mon. Not. R. Astron. Soc. 475, 2282–2305 (2018).

    ADS  Google Scholar 

  37. Cristallo, S., Straniero, O., Piersanti, L. & Gobrecht, D. Evolution, nucleosynthesis, and yields of AGB stars at different metallicities. III. Intermediate-mass models, revised low-mass models, and the ph-FRUITY interface. Astrophys. J. Suppl. 219, 40 (2015).

    ADS  Google Scholar 

  38. Bloecker, T. Stellar evolution of low and intermediate-mass stars. I. Mass loss on the AGB and its consequences for stellar evolution. Astron. Astrophys. 297, 727–738 (1995).

    ADS  Google Scholar 

  39. Bladh, S., Liljegren, S., Höfner, S., Aringer, B. & Marigo, P. An extensive grid of DARWIN models for M-type AGB stars. I. Mass-loss rates and other properties of dust-driven winds. Astron. Astrophys. 626, A100 (2019).

    ADS  Google Scholar 

  40. Girardi, L., Marigo, P., Bressan, A. & Rosenfield, P. The insidious boosting of thermally pulsing asymptotic giant branch stars in intermediate-age magellanic cloud clusters. Astrophys. J. 777, 142 (2013).

    ADS  Google Scholar 

  41. Maraston, C. et al. Evidence for TP-AGB stars in high-redshift galaxies, and their effect on deriving stellar population parameters. Astrophys. J. 652, 85–96 (2006).

    ADS  Google Scholar 

  42. Bruzual, A. & Charlot, G. Spectral evolution of stellar populations using isochrone synthesis. Astrophys. J. 405, 538–553 (1993).

    ADS  Google Scholar 

  43. Gaia Collaboration et al. The Gaia mission. Astron. Astrophys. 595, A1 (2016).

    Google Scholar 

  44. Gaia Collaboration et al. Gaia Data Release 2. Summary of the contents and survey properties. Astron. Astrophys. 616, A1 (2018).

    Google Scholar 

  45. Curtis, J. L., Wolfgang, A., Wright, J. T., Brewer, J. M. & Johnson, J. A. Ruprecht 147: the oldest nearby open cluster as a new benchmark for stellar astrophysics. Astron. J. 145, 134 (2013).

    ADS  Google Scholar 

  46. Tremblay, P.-E., Bergeron, P. & Gianninas, A. An improved spectroscopic analysis of DA white dwarfs from the Sloan Digital Sky Survey Data Release 4. Astrophys. J. 730, 128 (2011).

    ADS  Google Scholar 

  47. Bergeron, P. et al. A comprehensive spectroscopic analysis of DB white dwarfs. Astrophys. J. 737, 28 (2011).

    ADS  Google Scholar 

  48. Genest-Beaulieu, C. & Bergeron, P. A comprehensive spectroscopic and photometric analysis of DA and DB white dwarfs from SDSS and Gaia. Astrophys. J. 871, 169 (2019).

    ADS  Google Scholar 

  49. Fontaine, G., Brassard, P. & Bergeron, P. The potential of white dwarf cosmochronology. Publ. Astron. Soc. Pac. 113, 409–435 (2001).

    ADS  Google Scholar 

  50. Cukanovaite, E., Tremblay, P.-E., Freytag, B., Ludwig, H.-G. & Bergeron, P. Pure-helium 3D model atmospheres of white dwarfs. Mon. Not. R. Astron. Soc. 481, 1522–1537 (2018).

    ADS  Google Scholar 

  51. Tremblay, P. E., Cukanovaite, E., Gentile Fusillo, N. P., Cunningham, T. & Hollands, M. A. Fundamental parameter accuracy of DA and DB white dwarfs in Gaia data release 2. Mon. Not. R. Astron. Soc. 482, 5222–5232 (2019).

    ADS  Google Scholar 

  52. Cummings, J. D. & Kalirai, J. S. Improved main-sequence turnoff ages of young open clusters: multicolor UBV techniques and the challenges of rotation. Astron. J. 156, 165 (2018).

    ADS  Google Scholar 

  53. Bressan, A. et al. PARSEC: stellar tracks and isochrones with the PAdova and TRieste stellar evolution code. Mon. Not. R. Astron. Soc. 427, 127–145 (2012).

    ADS  Google Scholar 

  54. Marigo, P. et al. A new generation of PARSEC-COLIBRI stellar isochrones including the TP-AGB phase. Astrophys. J. 835, 77 (2017).

    ADS  Google Scholar 

  55. Asplund, M., Grevesse, N., Sauval, A. J. & Scott, P. The chemical composition of the Sun. Annu. Rev. Astron. Astrophys. 47, 481–522 (2009).

    ADS  Google Scholar 

  56. Reimers, D. Circumstellar absorption lines and mass loss from red giants. Mem. Soc. R. Sci. Liege 8, 369–382 (1975).

    ADS  Google Scholar 

  57. Pastorelli, G. et al. Constraining the thermally pulsing asymptotic giant branch phase with resolved stellar populations in the small magellanic cloud. Mon. Not. R. Astron. Soc. 485, 5666–5692 (2019).

    ADS  Google Scholar 

  58. Cranmer, S. R. & Saar, S. H. Testing a predictive theoretical model for the mass loss rates of cool stars. Astrophys. J. 741, 54 (2011).

    ADS  Google Scholar 

  59. Bowen, G. H. Dynamical modeling of long-period variable star atmospheres. Astrophys. J. 329, 299–317 (1988).

    ADS  Google Scholar 

  60. Bedijn, P. J. Pulsation, mass loss, and evolution of upper asymptotic giant branch stars. Astron. Astrophys. 205, 105–124 (1988).

    ADS  Google Scholar 

  61. Vassiliadis, E. & Wood, P. R. Evolution of low- and intermediate-mass stars to the end of the asymptotic giant branch with mass loss. Astrophys. J. 413, 641–657 (1993).

    ADS  Google Scholar 

  62. Lambert, D. L., Gustafsson, B., Eriksson, K. & Hinkle, K. H. The chemical composition of carbon stars. I—Carbon, nitrogen, and oxygen in 30 cool carbon stars in the galactic disk. Astrophys. J. Suppl. 62, 373–425 (1986).

    ADS  Google Scholar 

Download references

Acknowledgements

P.M., S.B., Y.C., L.G., G.P., M.T. and B.A. acknowledge the support from the ERC Consolidator Grant funding scheme (project STARKEY, grant agreement number 615604). P.-E.T. has received ERC funding under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 677706 – WD3D).

Author information

Authors and Affiliations

Authors

Contributions

P.M. designed and performed the theoretical research, ran the TP-AGB models and the population synthesis simulations, and provided the interpretation of the new IFMR data in terms of stellar evolution. J.D.C. performed the Keck observations, processed the data, analysed the cluster parameters, spectroscopically analysed the DA WDs and determined memberships. J.L.C. identified the likely WD candidates for observations and assisted with the cluster-parameter analysis. J.K. coordinated the observational and theoretical work and provided expertise. P.-E.T. provided the DA WD atmospheric models and fitting program and his expertise. E.R.-R. assisted with Keck observations. P.B. provided the DB WD atmospheric models and fit the DB parameters. S.B. provided expertise and help in implementing the mass-loss grid of dynamical atmospheres for carbon stars in the COLIBRI code. Y.C., A.B., L.G., G.P. and M.T. contributed to the development of the stellar models and the discussion of the results. S.C. contributed his WD photometric analysis expertise and his publicly available Python 3 module was used for the photometric-based derivation of WD parameters. B.A. provided expertise and the molecular opacity data to model the atmospheres of carbon stars. P.D.T. implemented the WD models in the populations synthesis simulations.

Corresponding author

Correspondence to Paola Marigo.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Astronomy thanks Krzysztof Gesicki, Iain McDonald and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Comparison between the semi-empirical IFMR and model results.

The semi-empirical data are shown with diamonds and error bars covering the range of ± 1 σ. Newly discovered and newly analysed WD data (see Table 1) are shown in green. a-b, Predictions for the whole (Mi, λ) grid of models. c-d, Selected models that are found to match the semi-empirical IFMR. The theoretical IFMR is colour-coded according to the values of the efficiency of the 3DU (a-c) and the photospheric C/O at the end of the TP-AGB phase (b-d).

Extended Data Fig. 2 Examples of theoretical IFMRs that fail to account for the kink in the semi-empirical IFMR.

a, Too high efficiency of the 3DU in low-mass stars: λ = 0.5 is assumed for all models that experience the 3DU. b, Mass loss insensitive to the photospheric chemical composition: the B95 mass-loss formula is applied to all models, irrespective of the photospheric C/O. The semi-empirical IFMR is the same as in Fig. 1, with error bars covering the range of ± 1 σ.

Supplementary information

Supplementary Information

Supplementary Figs. 1–6 and sections ‘The WD mass distribution’ and ‘Other supporting evidence: Galactic semi-regular variables’.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marigo, P., Cummings, J.D., Curtis, J.L. et al. Carbon star formation as seen through the non-monotonic initial–final mass relation. Nat Astron 4, 1102–1110 (2020). https://doi.org/10.1038/s41550-020-1132-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-020-1132-1

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing