Finite-field QED corrections to vacuum birefringence and magnetar polarization transport

[摘要] We study low-energy photon propagation in a constant magnetic field within the finite-field one-loop Heisenberg–Euler framework and apply the resulting mode-dependent refractive indices to magnetar polarization transport. In a centered-dipole model, the polarization-limiting radius is unchanged to better than 10-12\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$10^{-12}$$\end{document} because mode decoupling occurs at ∼102RNS\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\sim 10^2R_\textrm{NS}$$\end{document}, where B≪Bcr\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$B\ll B_\textrm{cr}$$\end{document}. Near the surface, however, the weak-field Cotton–Mouton expression overestimates the accumulated birefringent phase by up to a factor 2.9 at 1015\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$10^{15}$$\end{document} G. At the plasma–vacuum resonance, finite-field corrections reduce the resonance density by 32%\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$32\%$$\end{document} and raise the adiabatic conversion energy by 14%\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$14\%$$\end{document} for 1E 1547.0-5408; the corresponding changes are factors 2.6 and 1.37 for 1RXS J1708-4009, and factors 9.7 and 2.13 for SGR 1806-20, the latter controlled by the strong-field asymptote. The parallel-mode magnetic response remains positive and exhibits a broad maximum near 17Bcr\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$17B_\textrm{cr}$$\end{document}. Its strict O(α)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal O(\alpha )$$\end{document} expansion is monotonic, indicating that the detailed position and profile of the maximum are not controlled beyond the present approximation and require higher-loop assessment. These results identify vacuum-resonance observables as the most sensitive channel for testing finite-field QED in magnetars.

[发布日期] 2026-08-24