Surface Emission Properties of Strongly Magnetic Neutron Stars

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Abstract
We construct radiative equilibrium models for strongly magnetized (B 1013 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 1014 G, the emerging spectra are bluer than the blackbody corresponding to the effective temperature Teff with modified Planckian shapes because of the photon energy dependence of the magnetic opacities. However, vacuum polarization resonance significantly modifies the spectra for B ~ 1015 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 (5°) with respect to the normal and a broad maximum (fan beam) at intermediate angles (~20°-60°). 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 Teff-Tc relation for our models, where Tc is the local color temperature of the spectrum emerging from the neutron star surface, and find that Tc/Teff ranges between 1.1 and 1.8. We discuss the implications of our results for various thermally emitting neutron star models.