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We have used a revised Monte Carlo simulation to estimate light curves and energy spectra for gamma ray pulsars, under the assumption that these objects have nearly aligned rotational and magnetic axes. Our simulation is based on a Polar Cap model in which the gamma rays are due to photon-pair cascades initiated by curvature radiation above the magnetic polar caps (PCs). In the nearly-aligned rotator scenario, even sources whose light curves have two distinct peaks (Crab, Vela, Geminga) are due to emission produced near the rim of a single PC. If the inclination $\alpha \sim \theta_{pc}$, the peak-to-peak phase separation can have the large values ($\sim 0.4 \-- 0.5$) observed from these sources. We can also attribute their nonzero interpeak emission to cascades above the PC interior. Our new simulations allow for a finite electron acceleration zone above the PC, which can extend to a height of several stellar radii. Our best fits to the observed light curves are obtained from models in which the accelerated electrons have a quasi-uniform surface density over the PC interior and a sharp density increase of $\sim 3$) near the rim. We suggest that such a density function may result from acceleration of secondary pairs created near the rim, where the open magnetic field lines have their maximum curvature and hence are most likely to produce pairs below the acceleration cutoff height. We note that the combined effects of moderately enlarged PC radii and extended acceleration zones provide a solution to a major difficulty with standard PC models, namely their small emission beams (and hence small detection probabilities). We show that our model results for Vela can reproduce key features of both the light curves and the phase-resolved energy spectra. Finally, we consider constraints imposed on nearly-aligned rotator models by observations at other wavelengths (radio, optical, X-ray).
