Angular structure of finite-field vacuum birefringence in magnetars
Abstract
Vacuum birefringence in a strong magnetic field is often modelled by combining the finite-field splitting for perpendicular propagation with the familiar sin2θ 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/Bcr≤100, 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.
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BibTeX
@misc{abbassi2026angular,
title = {{Angular structure of finite-field vacuum birefringence in magnetars}},
author = {Shahram Abbassi and S. R. Valluri},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38573},
eprint = {2609.38573},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38573},
}
RIS
TY - UNPB
TI - Angular structure of finite-field vacuum birefringence in magnetars
AU - Shahram Abbassi
AU - S. R. Valluri
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38573
UR - https://arxiv.org/abs/2609.38573
AB - 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_cr≤100, 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.
ER -