Analyzing X-ray pulsar profiles: Geometry and beam pattern of Hercules X-1

We report on our analysis of a large sample of energy-dependent pulse profiles of the X-ray binary pulsar Hercules X-l. We iind that all data are compatible with the assumption of a slightly distorted magnetic dipole held as sole cause of the asymmetry of the observed pulse profiles. Further, the analysis provides evidence that the emission from both poles is equal. We determine an angle Theta(m) < 20 degrees between the rotation axis and the local magnetic axis. One pole has an offset delta < 5 degrees from the antipodal position of the other pole. The beam pattern shows structures that can be interpreted as pencil- and fan-beam configurations. Since no assumptions on the polar emission are made, the results can be compared with various emission models. A comparison of results obtained from pulse profiles of different phases of the 35 day cycle indicates different attenuation of the radiation from the poles being responsible for the change of the pulse shape during the main-on state. These results also suggest the resolution of an ambiguity within a previous analysis of pulse profiles of Cen X-3, leading to a unique result for the beam pattern of this pulsar as well. The analysis of pulse profiles of the short-on state indicates that a large fraction of the radiation cannot be attributed to the direct emission from the poles. We give a consistent explanation of both the evolution of the pulse profile and the spectral changes with the 35 day cycle in terms of a warped precessing accretion disk.