The Infrared to Gamma-Ray Pulse Shape of the Crab Nebula Pulsar
  We analyze the pulse shape of the Crab Nebula pulsar in the near-infrared, optical, ultraviolet, X-ray, and gamma-ray bands, including previously unpublished ROSAT HRI observations. We show that, in addition to the previously known trend for the fluences of the Bridge and Peak 2 to increase with energy relative to the fluence of Peak 1, there is a small but statistically significant trend for both to decrease with energy relative to Peak 1 over the near-infrared range. We find that the phase separation between the two peaks of the pulse profile decreases nearly continuously as a function of energy over 7 decades of energy. We show that the peaks' full-width half-maxima are significantly variable over this energy range, but without any clear pattern to the variability. We find that the differences between the energy dependences of the leading and trailing edge half-width half-maxima of both peaks found by Eikenberry et al. (1996a) also continue over 7 decades of energy. We show that the cusped shape of Peak 2 reverses direction between the infrared/optical and X-ray/gamma-ray bands, while the cusped shape of Peak 1 shows weak evidence of reversing direction between the X-ray and gamma-ray bands. Finally, we find that many of the pulse shape parameters show maxima or minima at energies of 0.5-1 eV, implying that an important change in the pulsar emission is occuring near this energy. Many of these complex phenomena are not predicted by current pulsar emission models, and offer new challenges for the development of such models. 
Stephen S. Eikenberry and Giovanni G. Fazio