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Essential of Ultra Strong Magnetic field and Activity For Magnetars

Essential of Ultra Strong Magnetic field and Activity For Magnetars. Qiu-he Peng ( qhpeng@nju.edu.cn ) (Dept. of Astronomy, Nanjing University, China). < CSQCD II>, KIAA-PKU,Bejing, China, May 20-24, 2009. Observation. For AXPs ( A normalous X -ray P ulsars)

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Essential of Ultra Strong Magnetic field and Activity For Magnetars

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  1. Essential of Ultra Strong Magnetic field and Activity For Magnetars Qiu-he Peng(qhpeng@nju.edu.cn) (Dept. of Astronomy, Nanjing University, China) < CSQCD II>, KIAA-PKU,Bejing, China, May 20-24, 2009

  2. Observation For AXPs (Anormalous X-ray Pulsars) and SGRs (Soft Gamma Repeaters ) Ultra strong magnetic field  Long spin period and spin-down rate  Absorption line at 10 keV

  3. Activity of Magnetars Abnormal high X-ray luminosityFor AXP • Decaying pulsating tails of giant flares with energy 1044 ergs It can not be explained by loss of the rotational energy. It is guessed by transformed from the energy of the ultra strong magnetic field of the magnetars. Surface temperature (by observation): T > 107 K for AXP T~105-106 K (for usual pulsars) Why??

  4. Proposed Models for the ultra strong B • Duncan & Thompson (1992, 1993):α-Ωdynamo with initial spin period less than 3ms • Ferrario & Wickrammasinghe(2005)suggest that the extra-strong magnetic field of the magnetars descends from their stellar progenitor with high magnetic field core. • Vink & Kuiper (2006) suggest that the magnetars originate from rapid rotating proto-neutron stars. • Iwazaki(2005)proposed the huge magnetic field of the magnetars is some color ferromagnetism of quark matter. The question is still open!

  5. Idea of mine: 1) Origin of Ultra strong B:  Ferromagnetism of Anisotropic ( 3P2 ) neutron superfluid 2) Activity: Instability due to high Fermi energy of electrons under the ultra strong B

  6. Part I Origin of Ultra strong Magnetic Field Is from Ferromagnetism of Anisotropic ( 3P2 ) neutron superfluid

  7. Structure of a neutron star = (g/cm3) 107 104 1011 Inner crust nuclei with Extra-neutron rich 1014 5×1014 1S0NSV(isotropic) Core (1km) 3P2NSV(anisotropic) Protons(5-8)% ( Type II superconductor?) (normal) electron Fermi gas Quarks ?? NSV: Neutron superfluid vortices outer crust (crystal of heavy metal)

  8. Two kinds of Neutron Cooper pairs (Pauli matrix) A neutron has a spin : (1S0-Cooper pair of neutrons) Vector addition : Total spin of a Cooper pair of neutrons: 3P2-Cooper pair of neutrons: (Projection along the external magnetic field)

  9. 1S0&3PF2Neutron superfluid (BEC based superfluidity ) 1S0 neutron Cooper pair: S=0, isotropic Energy gap : △(1S0) ≥ 0, 1011 < ρ(g/cm3) < 1.4×1014 △(1S0)≥2MeV 7×1012 <ρ(g/cm3)< 5×1013 3P2 neutron Cooper pair: S =1, anisotropic, abnormal magnetic moment ~10-23 c.g.s. Energy gap: △n(3P2) ～0.05MeV (3.31014 <  (g/cm3) < 5.21014)

  10. Anisotropic 3P2 neutron superfluid Critical temperature:  Magnetic moment: A magnetic moment tends to point at the direction of appliedmagnetic field with lower energy due to the interaction of the magnetic field with the magnetic moment of the 3P2 neutron Cooper pair.

  11. Energy distribution of neutrons in the presence of a magnetic field

  12. Statistics • Hamiltonian: • Ensemble average: The Brillouin function .

  13. Energy gap --- Combing energy of a Cooper pair A key idea: The energy gap, Δ, is a combining energy of couple of of neutrons (the Cooper pair). It is a real energy, rather than the variation of the Fermi energy due to the variation of neutron number density. Corresponding momentum of the combing energy of the neutron Cooper pair is (in non-relativity)

  14. q Value How many neutrons have been combined into the 3P2 Cooper pairs? Since only particles in the vicinity of the Fermi surface contribute (Lifshitz et al. 1999), there is a finite probability q for two neutrons being combined into a Cooper pair.

  15. Total induced magnetic field by the 3P2 superfluid or

  16. From paramagnetism to ferromagnetism (B < 1013 gauss , T > 107 K ) Set  (Curea Temparature) Paramagnetism is not important when T>Tc Phase Transition From paramagnetism to ferromagnetism When T down to T→Tc and the induced magnetic is very strong 

  17. Increase of magnetic field of NS • The induced magnetic field for the anisotropic neutron superfluid increases with decreasing temperature due to More and more neutron 3P2 Copper pairs transfer into paramagneticstates. b) The region and then mass of anisotropic neutron superfluid is increasing with decreasing temperature

  18. Energy gapof the 3P2 neutron pair(Elgagøy et al.1996, PRL, 77, 1428-1431)

  19. Theup limit of the magnetic field for magnetars Conclusion: All assumptions with B > 31015 gauss are unrealistic.

  20. Part II: Instability and activity of magnetars are Caused by The increase of Fermi energy of electrons under ultra strong magnetic field

  21. pz Landau quantization n=5 p n=6 n=3 n=2 n=1  n=4 n=0

  22. pz p The overwhelming majority of neutrons congregate in the lowest levels n=0 or n=1, When The Landau column is a rather long cylinder along the magnetic filed, but it is very narrow. The radius of its cross section is p .

  23. Under the ultra strong magnetic field Landau column pz The Landau energy level is quantized when B  Bcr ( Bcr =4.4141013 gauss) p n: quantum number of the Landau energy level n=0, 1,2,3……

  24. Total Occupied number of electrons(1) We may calculate the total occupied number by two different ways: 1)Total electron number density: Ye: electron fraction The total number of state occupied by the electrons in a complete degenerate electron gas should be equal to the electron number due to the Pauli’s Exclusion Principle

  25. Total Occupied number of electrons(2) 2) Method in Statistical physics: State number in a volume element of phase space: Landau quantization

  26. Cont.

  27. Result

  28. Fermi energy of electrons in ultra strong magnetic field

  29. Magnetars are unstable due to the ultra high Fermi energy of electrons

  30. Basic idea When the energy of the electron near the Fermi surface is rather high (EF>60 MeV) Energy of the resulting neutrons will be rather high and they will react with the neutrons in the 3P2 Cooper pairs and will destroy these 3P2 Cooper pairs . It will cause the anisotropic superfluid disappear and then the magnetic field induced by the 3P2 Cooper pairs will also disappear.

  31. Total thermal energy Average energy of outgoing neutrons after breakdown of the 3P2 Cooper pairs It will be transfer into thermal energy. Total thermal energy will be released after all 3P2 Cooper being breaked up

  32. Life time of magnetar activity X ray luminosity of AXPs It may be maintained ~ 107 -108 yr

  33. Phase Oscillation Afterwards, Revive to the previous state just before formation of the 3P2 neutron superfluid.  Phase Oscillation .

  34. Questions? • Detail process: The rate of the process • Time scale ?? • 2. What is the evolution of the previous instable process • of the magnetars? • 3. What is the real maximum magnetic field of the magnetars? • 4. How long is the period of oscillation above? • 5. How to compare with observational data • 6. Estimating the appearance frequency of AXP and SGR ? • A further work of mine: • “Heating by 3P2 Neutron Superfluid Votexes and Glitch of Pulsars Due to the Oscillation between A and B phase of Anisotropic superfluid”. (It Will be contributed to the conference on <Pulsars> next year)

  35. Thanks

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