Photon Propagation through Magnetar-Hosted Axion Clouds: Time Delays and Polarimetric Constraint

Temporal offsets between Gamma-Ray Bursts (GRBs) and high-energy neutrinos provide a useful probe of propagation effects in extreme astrophysical environments. We investigate whether such offsets can be generated by photon propagation through dense axion clouds gravitationally bound to magnetars. Working within axion electrodynamics, at the higher-loop vacuum-polarization effects, equivalent to the nonlinear Euler-Heisenberg theory in order to enhance the magnetic field effect extended by the axion sector, we derive the modified photon dispersion relations in the presence of a strong magnetic background and an oscillating axion field. We show that axion-photon mixing turns the magnetized vacuum into an anisotropic birefringent medium, leading to geometry-dependent deviations from luminal propagation and kinematic time delays that reach $\Delta t_{\perp}\simeq1.33\times10^{-12}\,\mathrm{s}$, for $\mathbf{k}\perp\mathbf{B}$. Although this effect is many orders of magnitude larger than the delays expected in diffuse astrophysical backgrounds, it remains far too small to account for the macroscopic offsets discussed in current multimessenger candidates. We show that the same birefringent medium constrains the survival of the intrinsic linear polarization of prompt GRB emission, yielding the environmental bound $g_{a\gamma\gamma}\lesssim6.02\times10^{-14}\,\mathrm{GeV}^{-1}$ for benchmark magnetar-scale parameters and axion masses near $m_a\sim10^{-4}\,\mathrm{eV}$. Magnetar-hosted axion clouds emerge as a complementary environment with dispersive transport and polarimetric observables. Although the dispersion of light through such an axion medium does not bring a sufficient delay of GRB to rule out its interpretation as Lorentz invariance violation, the other measurable quantities unambiguously indicate the presence of a chiral medium and jointly probe the details of axion electrodynamics.