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We have compared predictions of polar cap models for gamma-ray pulsars with recent observations of five sources (Crab, Vela, Geminga, PSR 1706-44, PSR 1055-52) by the EGRET detector on board the Compton Gamma Ray Observatory. We have derived estimates of energy spectra and pulse profiles from a revised Monte Carlo simulation of pair cascades above the magnetic poles. We find that the polar cap model with parameters close to conventional estimates yields spectra compatible with the observations reported to date, which all resemble power laws from about 50 MeV up to several GeV. Above a few GeV the polar cap model predicts cutoffs (as yet unconfirmed but possibly suggested by the observations) which are primarily sensitive to surface magnetic field strength. However, the standard polar cap model parameters predict pulse profiles with smaller duty cycles than those observed, and require nearly orthogonal rotators to produce double pulses. We have examined the dependence of the predicted pulse profiles on the model parameters, and we find that some departure from the simplest polar cap geometry (pure dipole field, standard polar cap radius, uniform primary current flow, nonextended acceleration zone) is required to match the observed profiles. We show that increasing the radius and/or height of the acceleration zone can result in improved fits to the pulse duty cycles.
