Outer-gap vs. Slot-gap Models for Pulsar High Energy Emissions: The Case of the Crab Pulsar

We analytically examine the capabilities of rotation-powered pulsars as the sources of gamma-rays and show that their phase-averaged gamma-ray flux is proportional to the product of the spin-down flux and the gap trans-field thickness cubed irrespective of the emission models. Applying the scheme to the Crab pulsar, we demonstrate that the outer-gap model reproduces the observed GeV fluxes and that the slot-gap model reproduces at most twenty per cent of the observed fluxes because of the small trans-field thickness. An implication on the relationship between the gamma-ray and the spin-down fluxes is discussed.