Radiative properties of magnetic neutron stars with metallic surfaces and thin atmospheres

The goal of this work is to develop a simple analytic description of the emission properties (spectrum and polarization) of the condensed, strongly magnetized surface of neutron stars. We have improved the method of van Adelsberg et al. (2005) (arXiv:astro-ph/0406001) for calculating the spectral properties of condensed magnetized surfaces. Using the improved method, we calculate the reflectivity of an iron surface at magnetic field strengths B \sim (10^{12} - 10^{14}) G, with various inclinations of the magnetic field lines and radiation beam with respect to the surface and each other. We construct analytic expressions for the emissivity of this surface as functions of the photon energy, magnetic field strength, and the three angles that determine the geometry of the local problem. Using these expressions, we calculate X-ray spectra for neutron stars with condensed iron surfaces covered by thin partially ionized hydrogen atmospheres. We develop simple analytic descriptions of the intensity and polarization of radiation emitted or reflected by condensed iron surfaces of neutron stars with strong magnetic fields typical for isolated neutron stars. This description provides boundary conditions at the bottom of a thin atmosphere, which are more accurate than previously used approximations. The spectra calculated with this improvement show absorption features different from those in simplified models. The approach developed in this paper yields results that can facilitate modeling and interpretation of the X-ray spectra of isolated, strongly magnetized, thermally emitting neutron stars.