To the Problem of Magnetic
Fields and Spin Polarization of
Nucleons in Astrophysics
A.I. Sery,
Brest State A.S. Pushkin University (Brest, Belarus)
XII Gomel School «Actual Problems of
Microworld Physics» 01.08.2013
I. The object and subject of
investigation
p- and np-gas in astrophysics
np-mixture at SN-II (with short lifetime)
(Bruenn, S.W. Recent 2D/3D Core-Collapse Supernovae
Simulations Results Obtained with the CHIMERA Code /
S.W. Bruenn et al. //physics.fau.edu)
Possible states of H in WD and SN-II
In spite of that, the models of degenerate
ep- and enp-gases should be also
considered as an approximation
Spontaneous nucleon spin polarization (leading to
magnetization) can be based on nuclear
pseudomagnetism, exchange and correlation
corrections. What is important here:
• V.G. Baryshevsky and M.I. Podgoretzky predicted
nuclear pseudomagnetism in 1964; After that V. G.
Baryshevsky proposed the idea that spin-polarized
state of nucleon system can turn out energetically
preferrable in comparison with non-polarized one;
Experiments in 1970s showed that nuclear
pseudomagnetic field exceeds ordinary
“polarizational” magnetic field by 2 orders;
• Is spontaneous spin polarization possible at SN II
explosions?
• Terrestrial ferromagnetism is mainly due to
exchange energy of electrons; at astrophysical
densities it seems to be impossible;
• Is ferromagnetism possible for proton gas due to
exchange energy of protons in astrophysics?
Basic known explanations of MF of WD and SN-II.
New questions for WD (DAP, DAH) and SN-II:
• Is ferromagnetism of nucleons possible?
• Can it be an additional explanation of magnetic
fields?
Some papers on MF of WD
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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.
Some papers on MF of SN
• 1. Steven A. Balbus and John F. Hawley.
Instability, turbulence, and enhanced
transport in accretion disks. Rev. Mod.
Phys. 70, 1–53 (1998)
• 2. Shizuka Akiyama and
J. Craig Wheeler. The Nonmonotonic
Dependence of Supernova and
Compact Remnant Formation on
Progenitor Rotation. The Astrophysical
Journal, 629:414-421, 2005 August 10
II. Methods and approximations
Restrictions imposed on our model
Metallization density (perhaps, overestimated)
Dirac delta, or Fermi pseudopotential, is used
for nuclear interaction (it is enough for
densities considered here)
Calculations for p- or np-Stoner criterion (1
non-degenerate or mixture of 2 degenerate
Fermi-gases): special algorithm was
developed on the basis of the algorithm for 1
degenerate Fermi-gas:
• L.S. Levitov, A.V. Shitov. Green
Functions. Tasks and solutions. Moscow,
Fizmatlit, 2003 [in Russian].
Stoner (ferromagnetism) criterion
formulations
III. Stoner criterion for
degenerate np-mixture
Energy density terms for degenerate
np-gas
Using the methods mentioned above, we obtain
Stoner criterion (w<0) for degenerate np-gas
What is possible in WDs (left) and
at SN-II explosions (left and right);
ferromagnetism is above the curves
Corresponding FM densities (table)
Magnetic fields of SN (though it’s better
to consider non-degenerate np-system
The main conclusions on Part III
• Spontaneous spin polarization for degenerate np-Fermigas is, most likely, possible
• It can occur right after a SN II explosion, though npmixture in SN II is, most likely, non-degenerate
• It could be also possible in WD under neutronization
threshold if the medium in WD was not crystal
• There is only 1 region or ferromagnetism on (np,nn)diagram if only nuclear interaction is considered
• There are 2 regions or ferromagnetism on (np,nn)diagram if not only nuclear, but also Coulomb exchange
interaction are 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
You can find the details of the
calculations for part III in the article
(http://www.brsu.by/
science/vestnik-brgu)
IV. Stoner criterion for nondegenerate hydrogen
The condition of non-degeneration
Chemical potential of ideal gas
Energy density of hot ideal Fermi-gas
Exchange (Coulomb) energy
density
Correlation (Coulomb) energy
density (according to Vedenov and
Larkin formula)
Nuclear energy density
After some rearrangements we obtain Stoner
criterion (w<0) for non-degenerate hydrogen
Magnetic fields of WD
As for SN-II, it’s better to consider nondegenerate np-system because here B ~ 108 Gs
is predicted for pure H in SN-II
The main conclusions on Part IV
• Spontaneous spin polarization for hot proton gas in
outer layers of WDs and SN II is possible
• The density region of ferromagnetism is smaller in
comparison with degenerate hydrogen
• Magnetic fields of B~106-109 Gs probably cannot
be explained directly by proton spin polarization
though such a polarization can form initial magnetic
field B~104 Gs which can be amplified by other
mechanisms
• The question of magnetization at SN-II explosions
(in outer layers) should be considered for nondegenerate np-system because only B~108 Gs is
predicted for pure hydrogen
You can find the details of the
calculations for part IV in the article
(http://www.brsu.by/
science/vestnik-brgu)
Thank you for your attention !