On the Geometry of the X-Ray Emission from Pulsars. I. Model Formulation and Tests

X-ray pulsars are complex magnetized astronomical objects in which many different attributes shape the pulse profiles of the emitted radiation. For each pulsar, the orientation of the spin axis relative to our viewing angle, the inclination of the magnetic dipole axis relative to the spin axis, and the geometries of the emission regions all play key roles in producing its unique pulse profile. In this paper, we describe in detail a new geometric computer model for X-ray emitting pulsars and the tests that we carried out in order to ensure its proper operation. This model allows for simultaneous tuning of multiple parameters for each pulsar and, by fitting observed profiles, it has the potential to determine the underlying geometries of many pulsars whose pulse profiles have been cataloged and made public in modern X-ray databases.