Timing results of 22 years for PSR J0922+0638

We conducted a timing analysis of PSR J0922+0638 (B0919+06) using data from the Nanshan 26 m radio telescope and the MeerKAT telescope, spanning from January 2001 to March 2023. During this 22-year period, we discovered a previously unreported small glitch (glitch 1) before the well-known large glitch (glitch 2), occurring at $\mathrm{M}\mathrm{J}\mathrm{D}\sim 53325(3)$, with a frequency jump amplitude of $\mathrm{\Delta }\nu \mathrm{/}\nu \sim 0.79(6)\times {10}^{-9}$. We also identified ten slow glitch events, half of which were newly detected. These slow glitches occurred quasi-periodically, with an average interval of approximately 553(21) days, fractional frequency changes ranging from $\mathrm{\Delta }\nu \mathrm{/}\nu \sim 1.13(1)\times {10}^{-9}$ to $4.08(5)\times {10}^{-9}$, and a maximum fractional change in the first derivative of the frequency of $\mathrm{\Delta }\dot{\nu }\mathrm{/}\dot{\nu }\sim -4.6\times {10}^{-3}$. Additionally, our timing noise analysis reveals a change in the spectral index for noise power before and after glitch 2, with values of $-6.0$ and $-5.3$, respectively, likely due to this large glitch. Throughout the entire observation period, the first derivative of the spin frequency ($\dot{\nu }$) showed a periodic structure. The possible modulation period was estimated to be 537(24) days before the 700-day data gap at MJD 56716 and 600(58) days afterward. We discuss the periodic oscillations in pulsar rotation as a possible manifestation of spin-down noise and quasi-periodic slow glitches.