Inferring the origins of the pulsed γ-ray emission from the Crab pulsar with ten-year Fermi-LAT data

Context. The Crab pulsar is a bright gamma -ray source, which has been detected at photon energies up to similar to 1 TeV. Its phase-averaged and phase-resolved gamma -ray spectra below 10 GeV exhibit exponential cutoffs, while those above 10 GeV apparently follow simple power laws.Aims. We re-visit the gamma -ray properties of the Crab pulsar with ten-year Fermi Large Area Telescope (LAT) data in the range of 60 MeV-500 GeV. With the phase-resolved spectra, we investigate the origins and mechanisms responsible for the emissions.Methods. The phaseograms were reconstructed for different energy bands and further analysed using a wavelet decomposition. The phase-resolved energy spectra were combined with the observations of ground-based instruments, such as MAGIC and VERITAS, to achieve a larger energy converage. We fitted power-law models to the overlapping energy spectra from 10 GeV to similar to 1 TeV. In the fit, we included a relative cross-calibration of energy scales between air-shower-based gamma-ray telescopes with the orbital pair-production telescope from the Fermi mission.Results. We confirm the energy-dependence of the gamma -ray pulse shape and, equivalently, the phase-dependence of the spectral shape for the Crab pulsar. A relatively sharp cutoff at a relatively high energy of similar to 8 GeV is observed for the bridge-phase emission. The E> 10 GeV spectrum observed for the second pulse peak is harder than those for other phases.Conclusions. In view of the diversity of phase-resolved spectral shapes of the Crab pulsar, we tentatively propose a multi-origin scenario where the polar-cap, outer-gap, and relativistic-wind regions are involved.