Magnetized neutron star atmospheres: beyond cold plasma approximation

All the neutron star (NS) atmosphere models published so far have been calculated in the "cold plasma approximation", which neglects the relativistic effects in the radiative processes, such as cyclotron emission/absorption at harmonics of cyclotron frequency. Here we present new NS atmosphere models which include such effects. We calculate a set of models for effective temperatures T_eff =1-3 MK and magnetic fields B \sim 10^{10}-10^{11} G, typical for the so-called central compact objects (CCOs) in supernova remnants, for which the electron cyclotron energy E_{c,e} and its first harmonics are in the observable soft X-ray range. Although the relativistic parameters, such as kT_eff /(m_e c^2) and E_{c,e} /(m_e c^2), are very small for CCOs, the relativistic effects substantially change the emergent spectra at the cyclotron resonances, E \approx sE_{c,e} (s=1, 2,...). Although the cyclotron absorption features can form in a cold plasma due to the quantum oscillations of the free-free opacity, the shape and depth of these features change substantially if the relativistic effects are included. In particular, the features acquire deep Doppler cores, in which the angular distribution of the emergent intensity is quite different from that in the cold plasma approximation. The relative contributions of the Doppler cores to the equivalent widths of the features grow with increasing the quantization parameter b_eff = E_{c,e}/kT_eff and harmonic number s. The total equivalent widths of the features can reach \sim 150-250 eV; they increase with growing b_eff and are smaller for higher harmonics.