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

This article has been updated


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.

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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.

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 The pulsation periods are computed with fitting relations based on publicly available models that can be found at

Code availability

The stellar evolution codes PARSEC and COLIBRI are not publicly available. The mass-loss routine for carbon stars can be found at The code to compute the dust-grain growth in the outflows of AGB stars can be retrieved from The code used here to calculate photometry-based WD parameters is available from

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.


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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




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.

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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.

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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’.

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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).

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