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当前脉冲星领域一个重要的研究热点是磁星. 本文在朱翠等(Zhu C, Gao Z F, Li X D, Wang N, Yuan J P, Peng Q H
2016 Mod. Phys. Lett. A 311650070 )工作的基础上, 重新研究了磁星超强磁场下($B\gg B$ cr, B cr是电子的量子临界磁场)电子朗道能级的稳定性及其对电子压强的影响. 首先, 对弱磁场极限下($B\ll B$ cr) 中子星内部电子压强进行必要的回顾; 然后, 通过引入电子朗道能级稳定性系数 g ν和Dirac- δ函数, 推导出在超强磁场下修正的相对论电子压强 P e的表达式, 给出表达式适用条件: 物质密度 ρ≥ 10 7g·cm –3和 B cr≤ B< 10 17G (1 G = 10 –4T). 超强磁场通过修正相对论电子的相空间, 提高了电子数密度 n e, 而 n e的增加意味着 P e的增加. 利用修正的电子压强表达式, 讨论了超强磁场下费米子自旋极化现象、电子磁化现象以及超强磁场对物态方程的修正. 最后, 本文的结果与其他类似工作进行对比, 并对未来的工作进行展望. 本文的研究将为磁星以及强磁化白矮星的物态方程和热演化的探索提供极有价值的参考, 将为普通射电脉冲星等离子磁层数值模拟、高磁场脉冲星辐射机制等相关研究提供有用的信息.Magnetar is a kind of pulsar powered by magnetic field energy. The study of magnetars is an important hotspot in the field of pulsars. In this paper, according to the work of Zhu Cui, et al. (Zhu C, Gao Z F, Li X D, Wang N, Yuan J P, Peng Q H2016 Mod. Phys. Lett. A 311650070 ), we reinvestigate the Landau-level stability of electrons in a superhigh magnetic field (SMF),$B\gg B_{\rm cr}$ ( B cris a quantum critical magnetic field with a value of 4.414×10 13G), and its influence on the pressure of electrons in magnetar. First, we briefly review the pressure of electrons in neutron star (NS) with a weak-magnetic field limit ($ B\ll B $ cr). Then, we introduce an electron Landau level stability coefficient g νand a Dirac- δfunction to deduce a modified pressure formula for the degenerate and relativistic electrons in an SMF in an application range of matter density ρ≥ 10 7g·cm –3and B cr$ \ll $ B< 10 17G. By modifying the phase space of relativistic electrons, the SMF can enhance the electron number density n e, and reduce the maximum of electron Landau level number ν max, which results in a redistribution of electrons. As Bincreases, more and more electrons will occupy higher Landau levels, and the electron Landau level stability coefficient g νwill decrease with the augment of Landau energy-level number ν. By modifying the phase space of relativistic electrons, the electron number density n eincreases with the MF strength increasing, leading the electron pressure P eto increase. Utilizing the modified expression of electron pressure, we discuss the phenomena of Fermion spin polarization and electron magnetization in the SMF, and the modification of the equation of state by the SMF. We calculate the baryon number density, magnetization pressure, and the difference between pressures in the direction parallel to and perpendicular to the magnetic field in the frame of the relativistic mean field model. Moreover, we find that the pressure anisotropy due to the strong magnetic field is very small and can be ignored in the present model. We compare our results with the results from other similar studies, and examine their similarities and dissimilarities. The similarities include 1) the abnormal magnetic moments of electrons and the interaction between them are ignored; 2) the electron pressure relate to magnetic field intensity B, electron number density n eand electron Fermi energy$E_{{\rm{F}}}^{{\rm{e}}}$ , and the latter two are complex functions containing B; 3) with n eand$E_{{\rm{F}}}^{{\rm{e}}}$ fixed, P eincreases with Brising; 4) as Bincreases, the pressure-density curves fitted by the results from other similar studies have irregular protrusions or fluctuations, which are caused by the transformation of electron energy state from partial filling to complete filling at the ν-level or the transition of electrons from the νto the ( ν+1)-level. This phenomenon is believed to relate to the behavior of electrons near the Fermi surface in a strong magnetic field, which essentially reflects the Landau level instability. Finally, the future research direction is prospected. The present results provide a reference for future studies of the equation of state and emission mechanism of high- Bpulsar, magnetar and strongly magnetized white dwarf.-
Keywords:
- superhigh magnetic field/
- Landau level/
- magnetars/
- magnetization
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B$\ll $B* B>B* nN/fm–3 $ E_{\text{F}}^{\text{e}} $/MeV Pe/(MeV·fm–3) P/(MeV·fm–3) M/M⊙ $ E_{\text{F}}^{\text{e}} $/MeV Pe/(MeV·fm–3) P/(MeV·fm–3) M/M⊙ 0.0013 2.924 4.9×10–10 3.78×10–6 0.0289 3.351 8.41×10–10 3.79×10–6 0.0311 0.0211 23.49 2.03×10–6 6.79×10–5 0.0593 27.62 2.88×10–6 7.36×10–5 0.0613 0.0772 68.58 1.47×10–4 0.0021 0.0517 81.06 2.87×10–4 0.00258 0.0543 0.1332 107.89 9.04×10–4 0.0143 0.2904 128.65 0.00182 0.0179 0.2932 0.1554 120.90 0.0014 0.0229 0.4201 145.13 0.00295 0.0725 0.4241 0.2003 143.58 0.0028 0.0475 0.6884 175.48 0.00632 0.0861 0.6965 0.2338 158.31 0.0042 0.0724 0.8808 183.72 0.00762 0.0965 0.8912 0.3206 190.04 0.0087 0.1624 1.2945 251.49 0.0267 0.2105 1.3062 0.3556 200.78 0.0108 0.2092 1.4236 273.35 0.0372 0.2761 1.4327 0.4186 218.29 0.0151 0.3065 1.6071 312.72 0.0637 0.4211 1.6223 0.4746 231.98 0.0193 0.4068 1.7263 347.67 0.0974 0.5816 1.7412 0.5446 247.31 0.0249 0.5479 1.8312 391.12 0.1561 0.8278 1.8522 0.6076 259.75 0.0304 0.6880 1.8947 429.70 0.2264 1.0272 1.9132 0.6846 273.65 0.0374 0.8737 1.9444 456.80 0.2905 1.3092 1.9675 0.7266 280.73 0.0414 0.9809 1.9621 480.23 0.3551 1.4782 1.9853 0.8396 298.23 0.0528 1.2845 1.9830 526.73 0.5135 1.9521 2.0061 0.9156 318.40 0.0655 1.5925 1.9916 586.65 0.7478 2.5316 2.0342 
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nN/fm–3 ρ/(g·cm–3) B/G ne/cm–3 |M|/G |MB|/(dyn·cm–2) ΔP/(dyn·cm–2) P///(dyn·cm–2) 0.0013 2.535×1012 1.000×1014 1.051×1032 4.277×1011 4.277×1025 8.385×1026 1.196×1030 0.0211 3.992×1013 1.003×1014 5.689×1034 2.841×1013 2.845×1027 3.641×1027 3.324×1031 0.0722 1.014×1014 1.011×1014 1.418×1036 2.428×1014 2.485×1028 2.567×1028 8.147×1031 0.1332 2.521×1014 1.073×1014 5.520×1036 6.049×1014 6.964×1028 7.055×1028 5.651×1031 0.1554 2.940×1014 1.116×1014 7.781×1036 7.638×1014 9.508×1028 9.607×1028 2.509×1034 0.2003 3.789×1014 1.247×1014 1.301×1037 1.089×1015 1.796×1029 1.708×1029 2.719×1034 0.2338 4.423×1014 1.393×1014 1.744×1037 1.868×1015 2.604×1029 2.619×1029 3.049×1034 0.3206 6.065×1014 2.011×1014 3.017×1037 5.406×1015 8.143×1029 8.175×1029 6.645×1034 0.3556 6.727×1014 2.377×1014 3.563×1037 5.406×1015 1.285×1030 1.291×1030 8.716×1034 0.4185 7.917×1014 3.237×1014 4.572×1037 7.676×1015 2.485×1030 2.493×1030 1.329×1035 0.4746 8.978×1014 4.244×1014 4.580×1037 1.237×1016 5.203×1030 5.217×1030 1.836×1035 0.5447 1.031×1015 5.860×1014 6.647×1037 2.249×1016 1.318×1031 1.321×1031 2.613×1035 0.6076 1.145×1015 7.685×1014 7.704×1037 3.353×1016 2.577×1031 2.583×1031 3.243×1035 0.6846 1.295×1015 1.042×1015 9.012×1037 5.225×1016 5.445×1031 5.453×1031 4.133×1035 0.7265 1.375×1015 1.215×1015 9.725×1037 6.533×1016 7.932×1031 7.944×1031 4.675×1035 0.8386 1.586×1015 1.763×1015 1.160×1038 1.109×1017 1.955×1032 1.958×1032 6.165×1035 0.9156 1.774×1015 2.347×1015 1.342×1038 1.678×1017 3.938×1032 3.943×1032 7.996×1035 下载:
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