Abstract
We present a modified scenario of gamma-ray emission from pulsars within the framework of polar cap models. Our model incorporates possible acceleration of electron-positron pairs created in magnetospheres, and their subsequent contribution to gamma-ray luminosity L_\gamma. It also reproduces the empirical trend in L_\gamma for seven pulsars detected with Compton Gamma Ray Observatory (CGRO) experiments. At the same time it avoids basic difficulties (Nel et al. 1996, Arons 1996) faced by theoretical models when confronted with observational constraints. We show that the classical and millisecond pulsars form two distinct branches in the L_gamma - L_sd diagram (where L_sd is the spin-down luminosity). In particular, we explain why the millisecond pulsar J0437-4715 has not been detected with any of the CGRO instruments despite its very high position in the ranking list of spin-down fluxes (i.e. L_sd/D^2, where D is a distance). The gamma-ray luminosity predicted for this particular object is about one order of magnitude below the upper limit set by EGRET.
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