发表机构
Department of Physics and Astronomy, The University of Western Ontario（韦仕敦大学物理与天文系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究解析证明磁星强磁场真空双折射的因子化角模型在非垂直传播时系统性高估，给出修正的解析展开，为强磁化环境偏振输运提供基准。
AI 中文摘要
强磁场中的真空双折射通常通过将垂直传播的有限场分裂与熟悉的$\sin^2\theta$角因子相结合来建模。这种分离仅在最低响应阶精确成立。延续我们先前对双折射场强依赖性的研究，我们考察了局域海森堡-欧拉理论中完整单圈折射率的角依赖性。我们解析地证明，在正双折射分支上，通常的因子化形式系统性地高估了偏离垂直传播时的精确分裂。相对修正最大处靠近磁场方向，此时绝对双折射本身消失。紧凑的解析展开揭示了在整个磁星相关范围$B/B_{\rm cr}\le100$内修正的符号、标度及角位置，而独立的固有时计算验证了底层单圈系数。在中心偶极子应用中，对于中等磁星场，修正低于百分之一，但对于最强源可达几个百分点；表面平均和径向相位累积随着场远离恒星表面而减弱其物理权重。该结果分离了有限场振幅和角修正，为强磁化环境中的精确偏振输运提供了受控的解析基准。
英文摘要
Vacuum birefringence in a strong magnetic field is often modelled by combining the finite-field splitting for perpendicular propagation with the familiar $\sin^2θ$ angular factor. That separation is exact only at leading response order. Continuing our previous study of the field-strength dependence of the birefringence, we examine the angular dependence of the full one-loop refractive indices in the local Heisenberg--Euler theory. We show analytically that, on the positive-birefringence branch, the usual factorized form systematically overestimates the exact splitting away from perpendicular propagation. The relative correction is largest close to the magnetic-field direction, where the absolute birefringence itself vanishes. Compact analytic expansions expose the sign, scaling, and angular location of the correction throughout the magnetar-relevant range $B/B_{\rm cr}\le100$, while an independent proper-time calculation verifies the underlying one-loop coefficients. In centred-dipole applications the correction is sub-percent for moderate magnetar fields but reaches several percent for the strongest sources; surface averaging and radial phase accumulation reduce its physical weight as the field decreases away from the stellar surface. The result separates finite-field amplitude and angular corrections and provides controlled analytic benchmarks for precision polarization transport in strongly magnetized environments.
Commentsv1: 8 pages, 5 figures. Comments are welcome
