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The goal of this work is to develop a simple analytic description of theemission properties (spectrum and polarization) of the condensed, stronglymagnetized surface of neutron stars. We have improved the method of vanAdelsberg et al. (2005) (arXiv:astro-ph/0406001) for calculating the spectralproperties of condensed magnetized surfaces. Using the improved method, wecalculate the reflectivity of an iron surface at magnetic field strengths B\sim (10^{12} - 10^{14}) G, with various inclinations of the magnetic fieldlines and radiation beam with respect to the surface and each other. Weconstruct analytic expressions for the emissivity of this surface as functionsof the photon energy, magnetic field strength, and the three angles thatdetermine the geometry of the local problem. Using these expressions, wecalculate X-ray spectra for neutron stars with condensed iron surfaces coveredby thin partially ionized hydrogen atmospheres. We develop simple analyticdescriptions of the intensity and polarization of radiation emitted orreflected by condensed iron surfaces of neutron stars with strong magneticfields typical for isolated neutron stars. This description provides boundaryconditions at the bottom of a thin atmosphere, which are more accurate thanpreviously used approximations. The spectra calculated with this improvementshow absorption features different from those in simplified models. Theapproach developed in this paper yields results that can facilitate modelingand interpretation of the X-ray spectra of isolated, strongly magnetized,thermally emitting neutron stars.

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