Atmospheres and Spectra of Strongly Magnetized Neutron Stars

We construct atmosphere models for strongly magnetized neutron stars with surface fields $B\sim 10^{12}-10^{15}$ G and effective temperatures $T_{\rm eff}\sim 10^6-10^7$ K. The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars, including radio pulsars, soft gamma-ray repeaters, and anomalous X-ray pulsars. In our models, the atmosphere is composed of pure hydrogen or helium and is assumed to be fully ionized. The radiative opacities include free-free absorption and scattering by both electrons and ions computed for the two photon polarization modes in the magnetized electron-ion plasma. Since the radiation emerges from deep layers in the atmosphere with $\rho\ga 10^2$ g/cm$^3$, plasma effects can significantly modify the photon opacities by changing the properties of the polarization modes. In the case where the magnetic field and the surface normal are parallel, we solve the full, angle-dependent, coupled radiative transfer equations for both polarization modes. We also construct atmosphere models for general field orientations based on the diffusion approximation of the transport equations and compare the results with models based on full radiative transport. In general, the emergent thermal radiation exhibits significant deviation from blackbody, with harder spectra at high energies. The spectra also show a broad feature ($\Delta E/\Ebi\sim 1$) around the ion cyclotron resonance $\Ebi=0.63 (Z/A)(B/10^{14}{G})$ keV, where $Z$ and $A$ are the atomic charge and atomic mass of the ion, respectively; this feature is particularly pronounced when $\Ebi\ga 3k\Teff$. Detection of the resonance feature would provide a direct measurement of the surface magnetic fields on magnetars.