Pulse profiles and spectra of gamma ray pulsars in the polar cap model

Abstract

We investigate predictions for pulse profiles and spectra of gamma-ray pulsars in the polar cap curvature radiation-initiated cascade model. In this model, the gamma-ray beam is a hollow cone centered on the magnetic pole, producing either double-peaked or single-peaked pulse profiles depending on observer orientation. We have computed simulated distributions of pulse peak phase separation seen by observers at random orientation as a function of gamma-ray beam width and obliquity distribution. The observed distribution of pulse peak phase separation, which favors double-peaked pulses with phase separation near 0.4, can be matched assuming that most gamma-ray pulsars have obliquity < 45° and beam opening angles of around 30°. The gamma-ray spectra result from primary particle curvature radiation, softened by synchrotron radiation from one or more generations of electron-positron pairs. We have determined the generation number and predicted spectral index of gamma-ray pulsar cascades as a function of period and surface magnetic field. It is found that the spectral hardness should decrease with cascade generation number and increase with characteristic age, a trend observed for EGRET-detected pulsars.