Surface Emission Properties of Strongly Magnetic Neutron Stars

We construct radiative equilibrium models for strongly magnetized (B ∼> 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 ∼ < 10 14 G, the emerging spectra are bluer than the blackbody corresponding to the effective temperature, Teff, with modified Planckian shapes due to the photon-energy dependence of the magnetic opacities. However, vacuum polarization resonance significantly modifies the spectra for B ∼ 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 ( ∼ < 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 − 1.8. We discuss the implications of our results for various thermally emitting neutron star models. Subject headings: radiation mechanisms:thermal — stars:atmospheres — stars:magnetic fields — stars:neutron — X-rays:stars 1.