The shapes of atomic lines from the surfaces of weakly magnetic rotating neutron stars and their implications

Motivated by the report by Cottam et al. of iron resonance scattering lines in the spectra of thermonuclear bursts from EXO 0748 - 676, we have investigated the information about neutron star structure and the geometry of the emission region that can be obtained by analyzing the profiles of atomic lines formed at the surface of the star. We have calculated the detailed profiles of such lines, taking into account the star's spin and the full effects of special and general relativity, including light bending and frame dragging. We discuss the line shapes produced by rotational Doppler broadening and magnetic splitting of atomic lines for the spin rates and magnetic fields expected in neutron stars in low-mass X-ray binary systems. We show that narrow lines are possible even for rapidly spinning stars if the emission region or the line of sight are close to the spin axis. For most neutron stars in low-mass systems, magnetic splitting is too small to obscure the effects of special and general relativity. We show that the ratio of the star's mass to its equatorial radius can be determined to within 5% using atomic line profiles, even if the lines are broad and skewed. This is the precision required to constrain strongly the equation of state of neutron star matter. We show further that if the radius and latitude of emission are known to similar to 5% - 10% accuracy, then frame dragging has a potentially detectable effect on the profiles of atomic lines formed at the stellar surface.