A re-visit of the phase-resolved X-ray and gamma-ray spectra of the Crab pulsar

We use a modified outer gap model to study the multi-frequency phase-resolved spectra of the Crab pulsar. The emissions from both poles contribute to the light curve and the phase-resolved spectra. Using the synchrotron self-Compton mechanism and by considering the incomplete conversion of curvature photons into secondary pairs, the observed phase-averaged spectrum from 100 eV - 10 GeV can be explained very well. The predicted phase-resolved spectra can match the observed data reasonably well, too. We find that the emission from the north pole mainly contributes to Leading Wing 1. The emissions in the remaining phases are mainly dominated by the south pole. The widening of the azimuthal extension of the outer gap explains Trailing Wing 2. The complicated phase-resolved spectra for the phases between the two peaks, namely Trailing Wing 1, Bridge and Leading Wing 2, strongly suggest that there are at least two well-separated emission regions with multiple emission mechanisms, i.e. synchrotron radiation, inverse Compton scattering and curvature radiation. Our best fit results indicate that there may exist some asymmetry between the south and the north poles. Our model predictions can be examined by GLAST.

The Phase-resolved High Energy Spectrum of the Crab Pulsar

We present a modified outer gap model to study the phase-resolved spectra of the Crab pulsar. A theoretical double peak profile of the light curve containing the whole phase is shown to be consistent with the observed light curve of the Crab pulsar by shifting the inner boundary of the outer gap inwardly to $sim 10$ stellar radii above the neutron star surface. In this model, the radial distances of the photons corresponding to different phases can be determined in the numerical calculation. Also the local electrodynamics, such as the accelerating electric field, the curvature radius of the magnetic field line and the soft photon energy, are sensitive to the radial distances to the neutron star. Using a synchrotron self-Compton mechanism, the phase-resolved spectra with the energy range from 100 eV to 3 GeV of the Crab pulsar can also be explained.