PULSAR X-RAY AND GAMMA-RAY PULSE PROFILES - CONSTRAINT ON OBLIQUITY AND OBSERVER ANGLES

We model the thermal X-ray profiles of Geminga, Vela, and PSR 0656+14, which have also been detected as gamma-ray pulsars, to constrain the phase space of obliquity and observer angles required to reproduce the observed X-ray pulsed fractions and pulse widths. These geometrical c onstraints derived from the X-ray light curves are explored for variou s assumptions about surface temperature distribution and flux anisotro py caused by the magnetized atmosphere. We include curved spacetime ef fects on photon trajectories and the magnetic field. The observed gamm a-ray pulse profiles are double peaked with phase separations of 0.4-0 .5 between the peaks. Assuming that the gamma-ray profiles are due to emission in a hollow cone centered on the magnetic pole, we derive the constraints on the phase space of obliquity and observer angles, for different gamma-ray beam sizes, required to produce the observed gamma -ray peak phase separations. We compare the constraints from the X-ray emission to those derived from the observed gamma-ray pulse profiles and find that the overlapping phase space requires both obliquity and observer angles to be smaller than 20 degrees-30 degrees, implying gam ma-ray beam opening angles of at most 30 degrees-35 degrees.