Geometry and pulse profiles of X-ray pulsars: Asymmetric relativistic fits to 4U 1538-52 and Vela X-1

Model calculations of inhomogeneous magnetized neutron star atmospheres are used to analyze the phase-dependent spectra of 4U 1538-52 and Vela X-1 taking into account general relativistic effects. A X² fitting procedure is used on the Ginga data for these objects to determine the geometry and the magnetic structure of the polar caps, as well as their size and location on the surface of the stars. Other parameters determined by the fit are the masses and radii of the neutron stars, the accretion rates, and the rotation and magnetic inclination angles including an azimuthal offset to reproduce the asymmetry of the pulse shapes. We find that general relativistic effects play a significant role in determining the derived cap sizes, the fluxes, and the observational appearance of the pulses. There is evidence that the polar caps are unequal and nonantipodal, suggesting either an off-center or bent magnetic axis, or a strong nondipole component. The magnetic field structure is approximated by a two-component model. The rotation axes are inferred to be moderately close to the mean magnetic axes and seen at large inclinations with respect to the line of sight.