We construct radiative equilibrium models for strongly magnetized ( B \gtrsim 10 ^ { 13 } G ) neutron-star atmospheres taking into account magnetic free-free absorption and scattering processes computed for two polarization modes .
We include the effects of vacuum polarization in our calculations .
We present temperature profiles and the angle- , photon energy- , and polarization-dependent emerging intensity for a range of magnetic field strengths and effective temperatures of the atmospheres .
We find that for B \lesssim 10 ^ { 14 } G , the emerging spectra are bluer than the blackbody corresponding to the effective temperature , T _ { eff } , with modified Planckian shapes due to the photon-energy dependence of the magnetic opacities .
However , vacuum polarization resonance significantly modifies the spectra for B \sim 10 ^ { 15 } G , giving rise to power-law tails at high photon energies .
The angle-dependence ( beaming ) of the emerging intensity has two maxima : a narrow ( pencil ) peak at small angles ( \lesssim 5 ^ { \circ } ) with respect to the normal and a broad maximum ( fan beam ) at intermediate angles ( \sim 20 - 60 ^ { \circ } ) .
The relative importance and the opening angle of the radial beam decreases strongly with increasing magnetic field strength and decreasing photon energy .
We finally compute a T _ { eff } - T _ { c } relation for our models , where T _ { c } is the local color temperature of the spectrum emerging from the neutron star surface , and find that T _ { c } / T _ { eff } ranges between 1.1 - 1.8 .
We discuss the implications of our results for various thermally emitting neutron star models .