M. M. Chaichian, B. A. Couto e Silva, B. L. Sánchez-Vega

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 the Euler-Heisenberg effective theory 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 $Δt_{\perp}\simeq1.33\times10^{-12}\,\mathrm{s}$ for orthogonal propagation. 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 further show that the same birefringent medium constrains the survival of the intrinsic linear polarization of prompt GRB emission, yielding the environmental bound $g_{aγγ}\lesssim6.02\times10^{-14}\,\mathrm{GeV}^{-1}$ for benchmark magnetar-scale parameters and axion masses near $m_a\sim10^{-4}\,\mathrm{eV}$. Magnetar-hosted axion clouds thus emerge as complementary environments in which dispersive transport and polarimetric observables jointly probe axion electrodynamics.