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Equilibrium models of relativistic stars with a toroidal magnetic field

机译:具有环形磁场的相对论恒星的平衡模型

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摘要

We have computed models of rotating relativistic stars with a toroidalmagnetic field and investigated the combined effects of magnetic field androtation on the apparent shape (i.e. the surface deformation), which could berelevant for the electromagnetic emission, and on the internal matterdistribution (i.e. the quadrupole distortion), which could be relevant for theemission of gravitational waves. Using a sample of eight different cold nuclearphysics equations of state, we have computed models of maximum field strength,as well as the distortion coefficients for the surface and the quadrupolardeformations. Surprisingly, we find that non-rotating models admit arbitrarylevels of magnetization, accompanied by a growth of size and quadrupoledistortion to which we could not find a limit. Rotating models, on the otherhand, are subject to a mass-shedding limit at frequencies well below thecorresponding ones for unmagnetized stars. Overall, the space of solutions canbe split into three distinct classes for which the surface deformation and thequadrupole distortion are either prolate and prolate, oblate and prolate, oroblate and oblate, respectively. We also derive a simple formula expressing therelativistic distortion coefficients, which allows one to compute the surfacedeformation and the quadrupole distortion up to significant levels of rotationand magnetization, essentially covering all known magnetars. Such a formulareplaces Newtonian equivalent expressions that overestimate the magneticquadrupole distortion by about a factor of 6 and are inadequate for stronglyrelativistic objects like neutron stars.
机译:我们已经计算了具有环形磁场的相对论恒星的旋转模型,并研究了磁场和旋转对表观形状(即表面变形)的组合效应,这可能与电磁辐射以及内部物质分布(即四极畸变)有关),这可能与引力波的发射有关。使用八个不同的冷核物理状态方程的样本,我们计算了最大场强以及表面和四极变形的畸变系数模型。出乎意料的是,我们发现非旋转模型接受任意水平的磁化强度,伴随着尺寸和四极畸变的增长,而我们找不到极限。另一方面,旋转模型在远低于未磁化恒星相应频率的频率上受到质量下降的限制。总的来说,解的空间可以分为三个不同的类别,它们的表面变形和四极畸变分别为扁长形和长扁形,扁长形和长扁形,扁圆形和扁长形。我们还推导了一个表达相对论失真系数的简单公式,该公式允许人们计算表面变形和四极畸变,直至显着水平的旋转和磁化,基本上涵盖了所有已知的磁星。这样的公式代替了牛顿等效表达式,后者将高四极矩的磁性高估了大约6倍,并且对于像中子星这样的强相对论物体来说是不够的。

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