Polarization modes in a strongly magnetized hydrogen gas

Propagation of high-frequency radiation in an anisotropic medium can be described in terms of two normal modes with different polarizations and different absorption coefficients. We investigate the properties of the normal modes in a strongly magnetized hydrogen gas for conditions expected in atmospheres of isolated neutron stars. We use the Kramers-Kronig relations to obtain the polarizability tensor for the strongly magnetized hydrogen. We derive and compute the polarizations and absorption coefficients of the normal modes from the polarizability tensor using both analytical approximations and numerical calculations. We find that the spectral features and anisotropy associated with the bound-bound and bound-free transitions in the magnetized hydrogen are manifested in the polarization characteristics, which affect substantially the spectral and angular dependences of the absorption coefficients of the normal modes and the transfer of radiation in neutron star atmospheres. There exist at least two critical frequencies at which, for any direction of propagation, either the normal mode polarizations are exactly linear or orientations of two polarization ellipses coincide with each other. For each of these frequencies there exists a direction of propagation for which the two normal modes are linearly polarized, and their polarizations and absorption coefficients fully coincide. The unusual properties of the normal modes should manifest themselves in the spectra, angular distribution, and polarization of the thermal-like radiation emitted from surface layers of neutron stars.