General Relativistic Effects on Magnetar Models of AXPs

General relativistic bending of light dramatically alters the variability of X-ray emission originating from the surfaces of ultramagnetic neutron stars. We construct radiative equilibrium models of such strongly magnetic cooling neutron stars with light-element atmospheres to compute the angle- and energy-dependent intensity emerging from their surfaces and find that the beaming of surface emission is predominantly non-radial. The combination of this radiation pattern with the calculations of light bending yields pulse amplitudes that vary non-monotonically with the neutron star compactness and the size of the emitting region. The significant suppression of the pulse amplitude for large emitting areas provides very strong constraints on the mechanisms that can simultaneously produce high periodic variability and X-ray luminosity. We apply these results to the thermally-emitting magnetar models of anomalous X-ray pulsars (AXPs), which are bright slowly-rotating X-ray sources with large pulse amplitudes. We use the observed fluxes and pulse amplitudes for all known AXPs and show that thermal emission from two antipodal regions on their surfaces, as predicted by some magnetar models, is inconsistent with these observed properties.