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Buoyant crystals halt the cooling of white dwarf stars

Nature volume 627, pages 286–288 (2024)Cite this article

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Abstract

White dwarfs are stellar remnants devoid of a nuclear energy source, gradually cooling over billions of years1,2 and eventually freezing into a solid state from the inside out3,4. Recently, it was discovered that a population of freezing white dwarfs maintains a constant luminosity for a duration comparable with the age of the universe5, signalling the presence of a powerful, yet unknown, energy source that inhibits the cooling. For certain core compositions, the freezing process is predicted to trigger a solid–liquid distillation mechanism, owing to the solid phase being depleted in heavy impurities6,7,8. The crystals thus formed are buoyant and float up, thereby displacing heavier liquid downward and releasing gravitational energy. Here we show that distillation interrupts the cooling for billions of years and explains all the observational properties of the unusual delayed population. With a steady luminosity surpassing that of some main-sequence stars, these white dwarfs defy their conventional portrayal as dead stars. Our results highlight the existence of peculiar merger remnants9,10 and have profound implications for the use of white dwarfs in dating stellar populations11,12.

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Fig. 1: Observational Gaia colour-magnitude Hertzsprung–Russell diagram of white dwarfs within 150 pc.
Fig. 2: Schematic representation of two scenarios of white dwarf crystallization.
Fig. 3: Observed and simulated distributions of high-mass white dwarfs along their cooling tracks.
Fig. 4: Evolving surface luminosity and central composition of high-mass white dwarf models.

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Data availability

The Gaia data are publicly available on the Gaia archive (https://gea.esac.esa.int/archive). Cooling sequences calculated for this work are provided at https://doi.org/10.5281/zenodo.10201676, as are the DQ model atmosphere synthetic magnitudes.

Code availability

The population-synthesis code is provided along with the cooling sequences at https://doi.org/10.5281/zenodo.10201676. We have opted not to make publicly available the highly specialized and multipurpose STELUM code because of its complexity.

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Acknowledgements

We thank the referees for their valuable comments that have improved this manuscript. We are grateful to P.-E. Tremblay for insightful discussions on the Q-branch problem and for a careful reading of our manuscript. We thank K. Shen, E. Bauer and H. Jia for helpful discussions that improved the work presented in this manuscript. This work has benefited from discussions at the KITP programme ‘White Dwarfs as Probes of the Evolution of Planets, Stars, the Milky Way and the Expanding Universe’ and was supported in part by the National Science Foundation under grant no. NSF PHY-1748958. A.B. is a Postdoctoral Fellow of the Natural Sciences and Engineering Research Council of Canada (NSERC) and also acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 101002408). S.B. was supported by a Banting Postdoctoral Fellowship and a CITA (Canadian Institute for Theoretical Astrophysics) National Fellowship. S.C. acknowledges the support from the Martin A. and Helen Chooljian Member Fund and the Fund for Natural Sciences at the Institute for Advanced Study, and thanks S. Yao for suggesting the comparison to the luminosity of M dwarfs and for her constant encouragement and inspiration.

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Author notes

  1. These authors contributed equally: Antoine Bédard, Simon Blouin

Authors and Affiliations

  1. Department of Physics, University of Warwick, Coventry, UK

    Antoine Bédard

  2. Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada

    Simon Blouin

  3. Institute for Advanced Study, Princeton, NJ, USA

    Sihao Cheng  (程思浩)

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Contributions

A.B., S.B. and S.C. planned this project, contributed new insights and research threads and wrote the manuscript. A.B. implemented the distillation process in the STELUM code and performed the cooling calculations. S.B. provided a prescription for the implementation of distillation, performed the population-synthesis simulations and subsequent data analysis and calculated model atmospheres. S.C. provided expertise on the observational properties of the Q branch and identified the importance of using a thin He layer and a realistic distillation profile. S.B. provided expertise on the physics of fractionation in dense plasmas. The listed order of the equally contributing authors was chosen randomly.

Corresponding authors

Correspondence to Antoine Bédard or Simon Blouin.

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Extended data figures and tables

Extended Data Fig. 1 Chemical evolution of a 1.15 M☉ white dwarf.

The 16O and 22Ne mass-fraction abundance profiles are shown at four different stages in the evolution of the star.

Extended Data Fig. 2 Distance distribution of white dwarfs.

Only high-confidence white dwarf candidates (PWD ≥ 0.9) in the Gaia EDR3 white dwarf catalogue69 are considered. The CDF is broken down into three MG bins that span the range of magnitudes covered in our analysis of the Q branch. For the faintest bin, the sample has a very high level of completeness up to a distance of 150 pc.

Extended Data Fig. 3 Modelled surface luminosity for different scenarios.

The surface luminosity is shown as a function of cooling age for 1.05, 1.15 and 1.25 M☉ C–O white dwarf models. The dotted lines correspond to the nominal case considered in Fig. 4a. The solid lines represent cooling sequences in which a standard composition7 is used instead of a post-merger profile (a), in which distillation is only partially completed (b) and in which X(22Ne) = 0.06 and distillation is turned off (c). Post-merger chemical profiles are assumed in panels b and c.

Extended Data Fig. 4 Effect of the composition on the predicted pile-up.

Same as Fig. 3 but with different assumptions for the composition of the extra-delayed C–O population.

Extended Data Fig. 5 Effect of a different implementation of distillation on the predicted pile-up.

Same as Fig. 3 but assuming partial completion of the distillation process. For the extra-delayed C–O population, our default post-merger composition profile is assumed.

Extended Data Fig. 6 Effect of distillation on the abundance profile.

The final 22Ne mass-fraction profile for a 1.15 M☉ white dwarf with an initial post-merger stratification is shown for two different scenarios. The composition profile is shown at the end of the crystallization process.

Extended Data Fig. 7 Effect of microscopic diffusion on the predicted pile-up.

Same as Fig. 3 but with X(22Ne) = 0.06 and no distillation (microscopic diffusion only). For the extra-delayed C–O population, our default post-merger composition profile is assumed.

Extended Data Fig. 8 Effect of the age distribution on the predicted pile-up.

Same as Fig. 3 but using a non-uniform stellar age distribution based on Mor et al.74.

Extended Data Fig. 9 Effect of the merger time delay on the predicted pile-up.

Same as Fig. 3 but assuming no merger time delay for all stars (a) and doubling the merger time delay used in our fiducial simulation (b).

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Bédard, A., Blouin, S. & Cheng, S. Buoyant crystals halt the cooling of white dwarf stars. Nature 627, 286–288 (2024). https://doi.org/10.1038/s41586-024-07102-y

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