中子星周围的多极电磁场：精确真空解及相关性质
Multipolar electromagnetic fields around neutron stars: exact vacuum solutions and related properties
摘要：
中子星周围的磁场拓扑是脉冲星磁层物理研究的关键问题之一。一个非常广泛的文献存在关于一个偶极磁场的假设，但很少取得进展，试图包括多极组件在一个自洽的方式。在本文中，我们研究的多极电磁场锚定在恒星的影响。给出了任意阶$l$的封闭形式的精确解析解，并将其应用于延迟点四极子（$l=2$），六极子（$l=3$）和八极子（$l=4$），延迟点偶极子（$l=1$）的推广.我们还比较了从每个多极的坡印廷通量，并表明自旋下降的光度取决于比率$R/r_{\rm L}$，$R$是中子星半径和$r_{\rm L}$的光柱半径。因此，制动指数也取决于$R/r_{\rm L}$。由于这样的多极场具有非常不同的拓扑结构，最重要的是较小的长度尺度相比，偶极场，特别是接近中子星，我们调查的变形的极冠引起的这些多极场。这种磁场可能对解释怀疑来自这些极冠的脉冲无线电发射以及从高能光变曲线拟合推导出的推断几何形状和磁场强度产生强烈影响。在四极场的情况下，我们强调了两极焦散线模型和我们的新多极焦散线模型之间的区别。在这方面，我们证明，工作与偶极场可以是非常误导。
英文摘要：
The magnetic field topology in the surrounding of neutron stars is one of the key questions in pulsar magnetospheric physics. A very extensive literature exists about the assumption of a dipolar magnetic field but very little progress has been made in attempts to include multipolar components in a self-consistent way. In this paper, we study the effect of multipolar electromagnetic fields anchored in the star. We give exact analytical solutions in closed form for any order $l$ and apply them to the retarded point quadrupole ($l=2$), hexapole ($l=3$) and octopole ($l=4$), a generalization of the retarded point dipole ($l=1$). We also compare the Poynting flux from each multipole and show that the spin down luminosity depends on the ratio $R/r_{\rm L}$, $R$ being the neutron star radius and $r_{\rm L}$ the light-cylinder radius. Therefore the braking index also depends on $R/r_{\rm L}$. As such multipole fields possess very different topology, most importantly smaller length scales compared to the dipolar field, especially close to the neutron star, we investigate the deformation of the polar caps induced by these multipolar fields. Such fields could have a strong impact on the interpretation of the pulsed radio emission suspected to emanate from these polar caps as well as on the inferred geometry deduced from the high-energy light-curve fitting and on the magnetic field strength. Discrepancies between the two-pole caustic model and our new multipole-caustic model are emphasized with the quadrupole field. To this respect, we demonstrate that working with only a dipole field can be very misleading.
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