标题： 扭动磁星磁层：一类半解析的强迫无旋转解 显示英文标题

标题： Twisted magnetar magnetospheres: a class of semi-analytical force-free non-rotating solutions

摘要： 磁层扭转，即具有环向分量的磁层，正受到密切关注，因为这种扭转被认为在中子星的行为中起着关键作用。 特别是，其耗散被认为是磁星活动的动力来源，并且是这些恒星演化中的一个重要因素。 我们展示了一类新的扭曲线对称的力自由磁层解。 通过引入类似于多极展开的假设来求解Grad-Shafranov方程。 我们得到一个层次化的常微分方程系统，其中低阶多极子源引高阶多极子。 我们表明可以得到解析近似，并且通常可以通过标准求解器数值计算解。 我们获得了一类初始条件具有很大灵活性的解，并证明其中一部分渐近趋于真空。 扭转并非局限于场线的某一部分。 这些解关于赤道对称，具有可反转的环向分量。 这种对称性由赤道电流片支持。 我们提供了某个特定解的一阶近似，该解由一个真空偶极子和一个由偶极子源引的环向磁场叠加而成，其中环向分量以 $1/r^4$ 衰减。 作为一个强多极解的例子，我们还展示了带有附加八极分量的情况。 显示英文摘要

摘要： Magnetospheric twists, that is magnetospheres with a toroidal component, are under scrutiny due to the key role the twist is believed to play in the behaviour of neutron stars. Notably, its dissipation is believed to power magnetar activity, and is an important element of the evolution of these stars. We exhibit a new class of twisted axi-symmetric force-free magnetospheric solutions. We solve the Grad-Shafranov equation by introducing an ansatz akin to a multipolar expansion. We obtain a hierarchical system of ordinary differential equations where lower-order multipoles source the higher-order ones. We show that analytical approximations can be obtained, and that in general solutions can be numerically computed using standard solvers. We obtain a class of solutions with a great flexibility in initial conditions, and show that a subset of these asymptotically tend to vacuum. The twist is not confined to a subset of field lines. The solutions are symmetric about the equator, with a toroidal component that can be reversed. This symmetry is supported by an equatorial current sheet. We provide a first-order approximation of a particular solution that consists in the superposition of a vacuum dipole and a toroidal magnetic field sourced by the dipole, where the toroidal component decays as $1/r^4$. As an example of strongly multipolar solution, we also exhibit cases with an additional octupole component.