Resonant Conversion of Photon Modes Due to Vacuum Polarization in a Magnetized Plasma: Implications for X-Ray Emission from Magnetars

It is known that vacuum polarization can modify the photon propagation modes in the atmospheric plasma of a strongly magnetized neutron star. A resonance occurs when the effect of vacuum polarization on the photon modes balances that of the plasma. We show that a photon (with energy $E\go$ a few keV) propagating outward in the atmosphere can convert from one polarization mode into another as it traverses the resonant density, $\rho_{res}\simeq Y_e^{-1}\eta^{-2}(B/10^{14} G)^2(E/1 keV)^2$ g cm$^{-3}$, where $Y_e$ is the electron fraction, and $\eta\sim 1$ is a slowly varying function of the magnetic field $B$. The physics of this mode conversion is analogous to the Mikheyev-Smirnov-Wolfenstein mechanism for neutrino oscillation. Because the two photon modes have vastly different opacities in the atmosphere, this vacuum-induced mode conversion can significantly affect radiative transport and surface emission from strongly magnetized neutron stars.