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.

White dwarfs as quantum crystals

Abstract

WHITE dwarfs are the most common endpoint of stellar evolution. Thermonuclear reactions have ceased, and the star settles into a compact object governed by relativistic, almost degenerate electrons. Bare nuclei of carbon and other heavier elements, normally considered as classical particles moving in the degenerate electron sea, are forced into a crystal lattice in the interior1 as the star cools, and a freezing front moves outward. Numerical simulations of the freezing of classical point charges in a uniform neutralizing background have been used to model the crystallization of white dwarfs2–4, but we show here that the classical approximation is not a good one: the energy per particle is significantly modified by quantum effects. The freezing process is then a transformation of a quantum liquid to a quantum solid, and the temperature of freezing may be reduced from the classical value. For lower mass stars particularly, the quantum corrections in liquid and solid seem to be comparable, and the physical conditions at freezing, classically typified by the ratio of the root-mean-square atomic displacement to the nearest-neighbour distance, are not greatly changed. Nevertheless, these new considerations may have an important effect on the cooling rate of white dwarfs, and thereby on their inferred evolution and ages.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1

    Shapiro, S. L. & Teukolsky, S. A. Black Holes, White Dwarfs, and Neutron Stars, Ch. 3 & 4, (Wiley. New York, 1983).

    Book  Google Scholar 

  2. 2

    Brush, S. G., Sahlin, H. L. & Teller, E. J. chem. Phys. 45, 2102 (1966).

    ADS  CAS  Article  Google Scholar 

  3. 3

    Hansen, J. P. Phys. Rev. A8, 3096 (1973).

    ADS  CAS  Article  Google Scholar 

  4. 4

    Stringfellow, G. S., De Witt, H. E. & Slattery, W. I. Phys. Rev. A41, 1105 (1990).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  5. 5

    Winget, D. E. et al. Astrophys. J. 315, L77 (1987).

    ADS  CAS  Article  Google Scholar 

  6. 6

    Garcia-Berro, E., Hernanz, M., Mochkovitch, R. & Isern, J. Astr. Astrophys. 193, 141 (1988).

    ADS  CAS  Google Scholar 

  7. 7

    Mochkovitch, R., Garcia-Berro, E., Hernanz, M., Isern, J. & Panis, J. F. Astr. Astrophys. 233, 456 (1990).

    ADS  Google Scholar 

  8. 8

    Canal, R., Isern, J. & Labay, J. Nature 296, L225 (1982); A. Rev. Astr. Astrophys. 28, 183 (1990).

    ADS  Article  Google Scholar 

  9. 9

    Abrikosov, A. JETP 12, 1254 (1961).

    Google Scholar 

  10. 10

    Salpeter, E. E. Astrophys. J. 134, 669 (1961).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  11. 11

    Mestel, L. & Ruderman, M. A. Mon. Not. R. astr. Soc. 136, 27 (1967).

    ADS  Article  Google Scholar 

  12. 12

    Van Horn, H. M. Astrophys. J. 151, 227 (1968).

    ADS  CAS  Article  Google Scholar 

  13. 13

    Lamb, D. Q. & Van Horn, H. M. Astrophys. J. 200, 306 (1975).

    ADS  CAS  Article  Google Scholar 

  14. 14

    Hansen, J. P. & Pollock, E. L. Phys. Rev. A8, 3110 (1973).

    Article  Google Scholar 

  15. 15

    Albers, R. C. & Gubernatis, J. E. Phys. Rev. B23, 2782 (1981); 33, 5180 (1986).

    ADS  Article  Google Scholar 

  16. 16

    Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Saunders, Philadelphia, 1976).

    MATH  Google Scholar 

  17. 17

    Kugler, A. A. Ann. Phys. 53, 133 (1969).

    ADS  Article  Google Scholar 

  18. 18

    Hansen, J. P. & Vieillefosse, P. Phys. Lett. A53, 187 (1975).

    Article  Google Scholar 

  19. 19

    Ceperley, D. & Alder, B. Phys. Rev. Lett. 45, 566 (1980).

    ADS  CAS  Article  Google Scholar 

  20. 20

    Mochkovitch, R. & Hansen, J. P. Phys. Lett. A73, 35 (1979).

    Article  Google Scholar 

  21. 21

    Nagara, H., Nagata, Y. & Nakamura, T. Phys. Rev. A36, 1859 (1987).

    ADS  CAS  Article  Google Scholar 

  22. 22

    Wood, M. A. & Winget, D. E. in White Dwarfs (ed. Wegner, G.) 282 (Springer, Berlin, 1989).

    Book  Google Scholar 

  23. 23

    Wood, M. A. thesis, Univ. of Austin (1990); Astrophys. J. (in the press).

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chabrier, G., Ashcroft, N. & DeWitt, H. White dwarfs as quantum crystals. Nature 360, 48–50 (1992). https://doi.org/10.1038/360048a0

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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