An Investigation of the state changes of PSR J2021+4026 and the Vela pulsar

We investigate the high energy emission activities of two bright gamma-ray pulsars, PSR~J2021+4026 and Vela. For PSR~J2021+4026, the state changes in the gamma-ray flux and spin-down rate have been observed. We report that the long-term evolution of the gamma-ray flux and timing behavior of PSR~J2021+4026 suggests a new gamma-ray flux recovery at around MJD~58910 and a flux decrease around MJD~59500. During this epoch, the staying time, the gamma-ray flux difference and spin-down rate are smaller than previous epochs in the same state. The waiting timescale of the quasi-periodic state changes is similar to the waiting timescale of the glitch events of the Vela pulsar. For the Vela pulsar, the quench of the radio pulse was in a timescale of $\sim0.2$~s after the 2016 glitch, and the glitch may disturb the structure of the magnetosphere. Nevertheless, we did not find any evidence for a long-term change in the gamma-ray emission properties using years of $Fermi$-LAT data, and therefore, no long-term magnetosphere structural change. We also conduct searching for photons above 100~GeV using 15-year $Fermi$-LAT data, and found none. Our results provide additional information for the relation between the state change of the gamma-ray emission and the glitch event.