ABSTRACT We report on long-term evolution of gamma-ray flux and spin-down rate of two bright gamma-ray pulsars, PSR J2021+4026 and Vela (PSR J0835−4510). PSR J2021+4026 shows repeated state changes in gamma-ray flux and spin-down rate. We report two new state changes, a first one from a low gamma-ray flux to a high flux that occurred around MJD 58910, and a second one from high to low flux that occurred around MJD 59510. We find that the flux changes associated with these two state changes are smaller than those determined in the previous events, and the waiting time of the new state change from the high gamma-ray flux to low gamma-ray flux is significantly shorter than previous events. Since the waiting time-scale of the quasi-periodic state changes of PSR J2021+4026 is similar to the waiting time-scale of the glitch events of the Vela pulsar, we search for the state change of the gamma-ray emission of the Vela pulsar to investigate the possibility that the glitching process is the trigger of the state change of PSR J2021+4026. For the Vela pulsar, the flux of the radio pulses briefly decreased around the 2016 glitch, suggesting that the glitch may have affected the structure of the magnetosphere. Nevertheless, we could not find any significant change of the gamma-ray emission properties using 15 yr of Fermi-LAT data. Overall, it seems inconclusive that a glitch-like process similar to that occurred to the Vela pulsar triggers the structure change of the global magnetosphere and causes state changes of PSR J2021+4026. Further and deep investigations to clarify the mechanism of the mode change for PSR J2021+4026 are required.
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