Polarization of neutron star surface emission: a systematic analysis

New-generation X-ray polarimeters currently under development promise to open a new window in the study of high-energy astrophysical sources. Among them, neutron stars (NSs) appear particularly suited for polarization measurements. Radiation from the (cooling) surface of an NS is expected to exhibit a large intrinsic polarization degree due to the star strong magnetic field (approximate to 10(12)-10(15) G), which influences the plasma opacity in the outermost stellar layers. The polarization fraction and polarization angle as measured by an instrument, however, do not necessary coincide with the intrinsic ones derived from models of surface emission. This is due to the effects of quantum electrodynamics in the highly magnetized vacuum around the star (the vacuum polarization) coupled with the rotation of the Stokes parameters in the plane perpendicular to the line of sight induced by the non-uniform magnetic field. Here, we revisit the problem and present an efficient method for computing the observed polarization fraction and polarization angle in the case of radiation coming from the entire surface of an NS, accounting for both vacuum polarization and geometrical effects due to the extended emitting region. Our approach is fairly general and is illustrated in the case of blackbody emission from an NS with either a dipolar or a (globally) twisted magnetic field.