Pulsar X‐Ray and Gamma‐Ray Pulse Profiles: Constraint on Obliquity and Observer Angles

Abstract

We model the thermal X-ray profilesof Geminga, Vela, and PSR 0656+14, which have also been detectedas gamma -ray pulsars, to constrain the phase space of obliquityand observer angles required to reproduce the observed X-ray pulsedfractions and pulse widths. These geometrical constraints derivedfrom the X-ray light curves are explored for various assumptionsabout surface temperature distribution and flux anisotropy caused bythe magnetized atmosphere. We include curved spacetime effects onphoton trajectories and the magnetic field. The observed gamma -raypulse profiles are double peaked with phase separations of 0.4-0.5between the peaks. Assuming that the gamma -ray profiles are due toemission in a hollow cone centered on the magnetic pole, we derive theconstraints on the phase space of obliquity and observer angles, fordifferent gamma -ray beam sizes, required to produce the observedgamma -ray peak phase separations. We compare the constraints fromthe X-ray emission to those derived from the observed gamma -raypulse profiles and find that the overlapping phase space requiresboth obliquity and observer angles to be smaller than 20 deg-30 deg,implying gamma -ray beam opening angles of at most 30 deg-35 deg.