Model atmospheres and X-ray spectra of bursting neutron stars

This paper presents the set of plane-parallel model atmosphere equations for a very hot neutron star (X-ray burst source). The model equations assume both hydrostatic and radiative equilibrium, and the equation of state of an ideal gas in local thermodynamic equilibrium (LTE). The equation of radiative transfer includes terms describing Compton scattering of photons on free electrons in fully relativistic thermal motion, for photon energies approaching $m_{\rm e} \, c^2$. Model equations take into account many bound-free and free-free energy-dependent opacities of hydrogen, helium, and the iron ions, and also a dozen bound-bound opacities for the highest ions of iron. We solve model equations by partial linearisation and the technique of variable Eddington factors. Large grid of H-He-Fe model atmospheres of X-ray burst sources has been computed for $10^7 \le T_{{\rm eff}}\le 3\times 10^7$ K, a wide range of surface gravity, and various iron abundances. We demonstrate that the spectra of X-ray bursters with iron present in the accreting matter differ significantly from pure H-He spectra (published in an earlier paper), and also from blackbody spectra. Comptonized spectra with significant iron abundance are generally closer to blackbody spectra than spectra of H-He atmospheres. The ratio of color to effective temperatures in our grid always remains in the range $1.2 < T_{\rm c}/T_{{\rm eff}}< 1.85$. The present grid of model atmospheres and theoretical X-ray spectra will be used to determine the effective temperatures, radii and $M/R$ ratios of bursting neutron stars from observational data.