Pulsed, Polarized X-ray Emission from Neutron Star Surfaces: the Effects of Vacuum Birefringence in the Magnetosphere

Abstract: Intense magnetic fields in the atmospheres of neutron stars render non-trivial angular dependence of intensity and polarization of soft X-ray emission originating from their surfaces. By tracking the complex electric field vector for each photon during its atmospheric transport and propagation in general relativistic and birefringent magnetospheres, our Monte Carlo simulation, named MAGTHOMSCATT, allows for capturing the complete polarization properties, including the intricate interplay between linearity and circularity. The new inclusion in MAGTHOMSCATT of quantum electrodynamical influences on polarization in the magnetosphere is presented. We simulate the pulsed and polarized X-ray emission from the outer layers of optically thick, fully ionized atmospheres of neutron stars, with a focus on the radiation emitted from extended polar caps of magnetars, which are the most highly magnetized neutron stars. Using the recent intensity pulse profile data for the magnetar 1RXS J11708-4009, we constrain the geometric parameters, namely the angles between the magnetic axis and the observer's viewing direction relative to the spin axis, as well as the sizes of emission regions. The distributions of these parameters and the best-fit configuration are provided. In addition, we discuss the important impacts of vacuum birefringence in the magnetosphere on increasing the linear polarization degree. A comparison with the case of a weakly magnetized neutron star, RX J0822.0-4300, is also discussed. Our simulation still needs further development, particularly to incorporate the vacuum resonance effect. Nevertheless, the formalism presented here can be employed to constrain geometric parameters for various types of neutron stars.