The First fermi-LAT Catalog of Sources Above 10 GeV reported evidence of pulsed emission above 25 GeV from 12 pulsars, including the Vela pulsar, which showed evidence of pulsation at $>37$ GeV energy bands. Using 62 months of fermi-LAT data, we anal
yzed the gamma-ray emission from the Vela pulsar and searched for pulsed emission above 50 GeV. Having confirmed the significance of the pulsation in 30-50 GeV with the H-test (p-value $sim10^{-77}$), we extracted its pulse profile using the Bayesian block algorithm and compared it with the distribution of the 5 observed photons above 50 GeV using the likelihood ratio test. Pulsation was significantly detected for photons above 50 GeV with p-value $=3times10^{-5}$ ($4.2sigma$). The detection of pulsation is significant above $4sigma$ at $>79$ GeV and above $3sigma$ at $>90$ GeV energy bands, making this the highest energy pulsation significantly detected by the LAT. We explore non-stationary outer gap scenario of the very high-energy emissions from the Vela pulsar.
There is a growing new class of young spin-down powered pulsars called GeV-quiet soft gamma-ray pulsar; (1) spectral turnover appears around~10MeV, (2) the X-ray spectra of below 20 keV can be described by power law with photon index around 1.2 and (
3) the light curve in X-ray/soft gamma-ray bands shows single broad pulse. Their emission properties are distinct from the normal gamma-ray pulsars, for which the spectral peak in $ u F_{ u}$ appears in GeV energy bands and the X-ray/gamma-ray light curves show sharp and double (or more) peaks. In this paper, we discuss that X-ray/soft gamma-ray emissions of the GeV-quiet soft gamma-ray pulsars are caused bythe synchrotron radiation of the electron/positron pairs, which are created by the magnetic pair-creation process near the stellar surface. In our model, the viewing geometry is crucial factor to discriminate between the normal gamma-ray pulsars and soft gamma-ray pulsars. Our model suggests that the difference between the magnetic inclination angle ($alpha$) and the Earth viewing angle ($beta$) of the soft gamma-ray pulsars is small, so that the synchrotron emissions from the high magnetic field region around the polar cap region dominates in the observed emissions. Furthermore, the inclination angle of the soft gamma-ray pulsar is relatively small, $alphaleq 30$~degree, and our line of sight is out of the gamma-ray beam emitted via the curvature radiation process in the outer gap. We also analysis the six year $Fermi$ data for four soft gamma-ray pulsars to determine the upper limit of the GeV flux.
