Transfer of Polarized Radiation in Strongly Magnetized Plasmas and Thermal Emission from Magnetars: Effect of Vacuum Polarization

We present a theoretical study of radiative transfer in strongly magnetized electron-ion plasmas, focusing on the effect of vacuum polarization due to quantum electrodynamics. This study is directly relevant to thermal radiation from the surfaces of highly magnetized neutron stars, which have been detected in recent years. Strong-field vacuum polarization modifies the photon propagation modes in the plasma and induces a ``vacuum resonance'' at which a polarized X-ray photon propagating outward in the neutron star atmosphere can convert from a low-opacity mode to a high-opacity mode and vice versa. The effectiveness of this mode conversion depends on the photon energy and the atmosphere density gradient. For a wide range of field strengths, B>~7×10¹³G, the vacuum resonance lies between the photospheres of the two photon modes, and the emergent radiation spectrum from the neutron star is significantly modified by the vacuum resonance. (For lower field strengths, only the polarization spectrum is affected.) Under certain conditions, which depend on the field strength, photon energy, and propagation direction, the vacuum resonance is accompanied by the phenomenon of mode collapse (at which the two photon modes become degenerate) and the breakdown of Faraday depolarization. Thus, the widely used description of radiative transfer based on photon modes is not adequate to treat the vacuum polarization effect rigorously. We study the evolution of polarized X-rays across the vacuum resonance and derive the transfer equation for the photon intensity matrix (Stokes parameters), taking into account the effect of birefringence of the plasma-vacuum medium, free-free absorption, and scatterings by electrons and ions.