We use a modified outer-gap model to study the multifrequency 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 selfCompton mechanism and by considering the incomplete conversion of curvature photons into secondary pairs, the observed phase-averaged spectrum from 100 eV to 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, the bridge, and leading wing 2, strongly suggest that there are at least two well-separated emission regions with multiple emission mechanisms-synchrotron radiation, inverse Compton scattering, and curvature radiation. Our best-fit results indicate that there may exist some asymmetry between the south and north poles. Our model predictions can be examined with GLAST.

The nonÈspherically symmetric transport equations and exact thermal evolution model are used to calculate the transient thermal response to pulsar glitches. The three possible forms of energy release from glitches, namely, the "" shell,ÏÏ "" ring,ÏÏ and "" spot ÏÏ cases, are compared. The X-ray light curves resulting from the thermal response to the glitches are calculated. Only the "" spot ÏÏ case and the "" ring ÏÏ case are considered because the "" shell ÏÏ case does not produce signiÐcant modulative X-rays. The magnetic Ðeld (B) e †ect, the relativistic light-bending e †ect, and the rotational e †ect on the photons being emitted in a Ðnite region are considered. Di †erent sets of parameters result in di †erent evolution patterns of light curves. We Ðnd that this modulated thermal X-ray radiation resulting from glitches may provide some useful constraints on glitch models.

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 ∼ 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.

The non-spherically symmetric transport equations and exact thermal evolution model are used to calculate the transient thermal response to pulsars. The three possible ways of energy release originated from glitches, namely the 'shell', 'ring' and 'spot' cases are compared. The X-ray light curves resulting from the thermal response to the glitches are calculated. Only the 'spot' case and the 'ring' case are considered because the 'shell' case does not produce significant modulative X-rays. The magnetic field ( B) effect, the relativistic light bending effect and the rotational effect on the photons being emitted in a finite region are considered. Various sets of parameters result in different evolution patterns of light curves. We find that this modulated thermal X-ray radiation resulting from glitches may provide some useful constraints on glitch models.