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Most models of anomalous X-ray pulsars (AXPs) account for the observed X-rayspectra and pulsations by means of radiation processes that occur on thesurfaces of neutron stars. For any such model, general relativistic deflectionof light severely suppresses the amplitude of the observed pulsations. Wecalculate the expected pulsation amplitudes of AXPs according to various modelsand compare the results with observations. We show that the high (<= 70%) pulseamplitudes observed in some AXPs can be accounted for only if the surfaceemission is localized (spot radius <40 degrees) and strongly beamed(cos^n[theta'] with n>2, where theta' is the angle to the normal). Theseconstraints are incompatible with those cooling and magnetar models in whichthe observed X-rays originate as thermal emission from the neutron-starsurface. Accretion models, on the other hand, are compatible with observationsfor a wide range of parameters. Finally, definitive conclusions cannot bereached on magnetospheric models, since their localization and beamingproperties are not well understood.Comment: 7 pages, 9 figures, submitted to The Astrophysical Journa

General Relativistic Constraints on Emission Models of Anomalous X‐Ray Pulsars