Atmosphere Models of Magnetized Neutron Stars: QED Effects, Radiation Spectra, and Polarization Signals

Abstract

Theoretical modeling of surface emission from magnetized neutron stars (NSs) requires proper treatment of QED effects, in particular the effect of photon mode conversion due to the ``vacuum resonance'' between plasma and vacuum polarization. Previous NS atmosphere models incorporated this effect approximately, using transfer equations for the photon modes which are inadequate near the vacuum resonance, particularly for field strengths around $B_l\simeq 7\times 10^{13}$ G, where the vacuum resonance occurs near the photosphere. In this paper, we provide an accurate treatment of the QED-induced mode conversion effect in NS atmosphere models, employing both the modal radiative transfer equations, coupled with an accurate mode conversion probability at the resonance, and the full evolution equations for the photon Stokes parameters. In doing so, we are able to quantitatively calculate the effects of vacuum polarization on the atmosphere emission spectra, beam patterns, and polarizations for the entire range of field strengths, $B=10^{12}-10^{15}$ G. We find that for NSs with $B\ga 2 B_l$, vacuum polarization reduces the widths of spectral features, and softens the hard spectral tail typical of magnetized atmosphere models. For $B\la B_l/2$, vacuum polarization does not change the emission spectra, but can significantly affect the polarization signals. We show that vacuum polarization induces a unique energy-dependent linear polarization signature, and that circular polarization can be generated in the magnetospheres of rapidly rotating NSs. We discuss the implications of our results for recent observations of thermally emitting isolated NSs and magnetars, as well as the prospects for future spectral and polarization observations.