General relativistic constraints on emission models of anomalous X-ray pulsars

Most models of anomalous X-ray pulsars (AXPs) account for the observed X-ray spectra and pulsations by means of radiation processes that occur on the surfaces of neutron stars. For any such model, general relativistic deflection of light severely suppresses the amplitude of the observed pulsations. We calculate the expected pulsation amplitudes of AXPs according to various models and compare the results with observations. We show that the high (≲ 70%) pulse amplitudes observed in some AXPs can be accounted for only if the surface emission is localized (spot radius < 40°) and strongly beamed (e.g., radially peaked with cosⁿ θ′ and n ≳ 2, where θ′ is the angle to the normal). These constraints are incompatible with those cooling and magnetar models in which the observed X-rays originate as thermal emission from the neutron star surface. Accretion models, on the other hand, are compatible with observations for a wide range of parameters. Finally, definitive conclusions cannot be reached on magnetospheric models, since their localization and beaming properties are not well understood.