Fermi γ-Ray Pulsars: Spectral and Generation Order Parameters

We examine the theory of generation order parameters. Three kinds of generation order parameters are introduced, which describe the production of high-energy γ photons in a cascade process scenario. We find a correlation between the average power-law photon index Γ and spin-down rate in 38 common FERMI γ-ray pulsars, and find that the third generation order parameter, which implies that the magnetic field may have the most significant effect on the high-energy γ photon absorption in the cascade processes, is the best one. The statistical work shows that the theory of generation order parameters can be applied to describe the the γ-ray pulsar radiation mechanisms in the cascade processes.