Pulse Profiles, Spectra and Polarization Characteristics of Non-Thermal Emissions from the Crab-Like Pulsars

Abstract

We discuss non-thermal emission mechanism of the Crab-like pulsars with both a two-dimensional electrodynamical study and a three-dimensional model. We investigate the emission process in the outer gap accelerator. In the two-dimensional electrodynamical study, we solve the Poisson equation of the accelerating electric field in the outer gap and the equation of motion of the primary particles with the synchrotron and the curvature radiation process and the pair-creation process. We show a solved gap structure which produces a consistent gamma-ray spectrum with EGRET observation. Based on the two-dimensional model, we conduct a three-dimensional emission model to calculate the synchrotron and the inverse-Compton processes of the secondary pairs produced outside the outer gap. We calculate the pulse profiles, the phase-resolved spectra and the polarization characteristics in optical to $γ$-ray bands to compare the observation of the Crab pulsar and PSR B0540-69. For the Crab pulsar, we find that the outer gap geometry extending from near the stellar surface to near the light cylinder produces a complex morphology change of the pulse profiles as a function of the photon energy. This predicted morphology change is quite similar with that of the observations. The calculated phase-resolved spectra are consistent with the data through optical to the $γ$-ray bands. We demonstrate that the 10$\sim$20 % of the polarization degree in the optical emissions from the Crab pulsar and the Vela pulsar are explained by the synchrotron emissions with the particle gyration motion.