Neutron stars (NSs) are formed in core-collapse supernovae. They are much more compact than WDs (roughly one solar mass packed in a 30 km diameter sphere). One of the most interesting questions concerns the equation-of-state (EOS) at super-nuclear densities encountered in NS cores. This is of basic physical interest. The mass-radius relation of NSs depends on the EOS, hence, from the observation of NS masses and radii we can empirically confirm or discard various EOS theories. One possibility to infer a NS radius is the analysis of its thermal surface emission spectrum. However, only a few NSs are known whose spectrum is not determined by the magnetospheric emission. These are the so-called Magnificent Seven (also called Isolated Neutron Stars, INSs, or X-ray Dim Isolated Neutron Stars, XDINSs), discovered by ROSAT. They exhibit broad X-ray absorption features which probably are proton- (or ion-) cyclotron lines hence, their magnetic fields are very strong (of the order 1015 Gauss).
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.
Another possibility to constrain the compactness of NSs is the gravitational redshift measurement of narrow atomic absorption lines in X-ray bursters. These are accreting neutron stars in binary systems, suffering a thermonuclear explosion on their surface. We are using our LTE and non-LTE codes to construct respective model atmospheres.