About the possibility of proton ferromagnetism in DA white dwarfs

1. About the possibility of proton ferromagnetism in DA white dwarfs A.I. Sery, Brest State A.S. Pushkin University (Brest, Belarus) V Young Scientists Conference «Problems of Theoretical Physics» N.N. Bogolyubov Institute for Theoretical Physics, Kyiv, 27.12.2013

2. I. The object and subject of investigation

3. Hydrogen in white dwarfs

4. Possible states of H in DA white dwarfs

5. Basic known explanations of MF of WD • 1. Hydromagnetic dynamo • 2. Accretion • 3. Rotation • 4. Common envelope with another star in a close binary system • 5. Magnetic flux conservation at contraction of initial star New questions for WD (DAP, DAH): • Is ferromagnetism of protons possible? • Can it be an additional explanation of magnetic fields?

6. Ferromagnetism can be based on different interactions where exchange forces and spin dependence take place. Let’s consider Coulomb and nuclear interactions as the most important ones

7. Some papers on MF of WD • 1. Angel, J.P.R. Magnetic White Dwarfs // J.P.R. Angel. // Ann. Rev. Astron. Astrophys. – 1978. – Vol. 16 – P. 487. • 2. Landstreet, J.D. The Magnetic Fields of Single White Dwarfs / J.D. Landstreet // White Dwarfs and Variable Degenerate Stars (IAU Colloq. No 53). Eds. H.M. Van Horn and V. Weidemann. – Rochester, New York: University of Rochester Press, 1979. • 3. Valyavin, G.G. Magnetic fields of white dwarfs // G.G. Valyavin, T.E. Burlakova, S.N. Fabrika and D.N. Monin // Astronomy Reports. – 2003. – Vol. 47, № 7 – P. 587–599. • 4. Jordan, S. The fraction of DA white dwarfs with kilo-Gauss magnetic fields. / S. Jordan, R. Aznar Cuadrado, R. Napiwotzki, H.M. Schmid, S.K. Solanki // arxiv.org/abs/astro-ph/0610875v2 – P. 1–10. • 5. Cumming, Andrew. Magnetic Field Evolution in Accreting White Dwarfs / Andrew Cumming // ASP Conference Series. – P. 1–13. • 6. Tout, Christopher A. The origin of the strongest magnetic fields in dwarfs. / Christopher A. Tout // Pramana – J. Phys. – July 2011. – Vol. 77, № 1. – P. 199–212. • 7. Liebert, James. The True Incidence of Magnetism Among Field White Dwarfs. / James Liebert, P. Bergeron and J.B. Holberg // arxiv.org/abs/astro-ph/0210319v2 – P. 1–16. • 8. Nordhaus, Jason. Formation of high-field magnetic white dwarfs from common envelopes. / Jason Nordhaus [et al.] // www.pnas.org/cgi/doi/10.1073/pnas.1015005108 – P. 1–6. • 9. Norton, A.J. The spin periods and magnetic moments of white dwarfs in magnetic cataclysmic variables / A.J. Norton, G.A. Wynn, and R.V. Somerscales // Astrophysical Journal. – 2004. – 614(1, Par). – P. 349–357.

8. II. Methods and approximations

9. Range of hydrogen densities

10. Dirac delta, or Fermi pseudopotential, is used for nuclear interaction (it is enough for the densities considered here). The expression is similar for cold and hot gases

11. Special algorithm for Stoner criterion calculation (for cold and hot gases with long- and short-range interactions) was developed on the basis of the algorithm for 1 cold Fermi-gas with contact interaction only: • L.S. Levitov, A.V. Shitov. Green Functions. Tasks and solutions. Moscow,Fizmatlit, 2003 [in Russian].

12. Stoner (ferromagnetism) criterion formulations

13. III. Stoner criterion for hydrogen in T=0 K approximation

14. Energy density terms for cold p-gas

15. Using the methods mentioned above, we obtain Stoner criterion (w<0) for cold p-gas

16. Corresponding densities for ferromagnetism

17. The main conclusions on Part III • Spontaneous spin polarization for cold p-Fermi-gas is, most likely, possible • It could be also possible in WD under neutronization threshold if the medium in WD was not crystal • Ferromagnetism is impossible for pure hydrogen if only nuclear interaction is considered • Ferromagnetism is possible for pure hydrogen if not only nuclear, but also Coulomb exchange interaction is considered • Coulomb correlation energy reduces the positive effect of Coulomb exchange energy, but net effect for ferromagnetism is still more favourable in comparison with the case when only nuclear energy is considered

18. IV. Stoner criterion for non-degenerate hydrogen

19. The condition of non-degeneration

20. Chemical potential of ideal gas

21. Energy density of hot ideal Fermi-gas

22. Exchange (Coulomb) energy density

23. Correlation (Coulomb) energy density (according to Vedenov and Larkin formula)

24. Nuclear energy density

25. After some rearrangements we obtain Stoner criterion (w<0) for hot hydrogen

26. Graphical results

27. Magnetic fields in outer layers of WDs

28. Magnetic fields in inner layers of WDs

29. The main conclusions on Part IV Spontaneous spin polarization for hot proton gas in outer layers of WDs is possible The density region of ferromagnetism is smaller in comparison with cold hydrogen Magnetic fields of B~106-109 Gs probably canbe explained by proton spin polarization if such a polarization forms initial magnetic field B~104 Gs which can be amplified in inner cold crystal layers; such situation is possible only at accretion of hydrogen onto a cold WD

30. Thank you for your attention !