Atmospheric modeling enables the temperature determination and, if the distance is known, the determination of the NS radius. However, modeling is rather challenging. We need to account for polarized radiation transfer, gravitational light bending, and effects on radiation like vacuum polarization and mode conversion. We even have to account for the possibility that there exists no atmosphere at all, i.e., that we just see the emission from a hot, magnetized, solid iron surface. There are hints that a relatively thin atmosphere can exist on top of the solid surface. It is optically thick only for photons in particular energy ranges and polarisation modes, so that we see a complicated mix of atmospheric and iron-surface photons. We have developed a new model code that can account for all of these effects and complications.
In addition to the isolated neutron stars, we also can observe thermal surface emission from Central Compact Objects (CCOs) in supernova remnants. Their magnetic fields are much weaker (<1011 Gauss, inferred from rotation-frequency decrease). We believe that the X-ray absorption features discovered in the CCO 1E1207.4-5209 are electron-cyclotron lines. They are reproduced by our models, however, only with newly incorporated quantum effects on the free-free opacity.