The Spin-down State Change and Mode Change Associated with Glitch Activity of PSR B2035+36

We presented timing results of PSR B2035+36 using ~9-yr observations with the Nanshan 25-m radio telescope. PSR B2035+36 was reported to exhibit significant changes in pulse profile correlated with spin-down state variations. We found that the pulsar underwent a glitch with a jump in the frequency of $Δν\sim12.4(5)\, \rm nHz$ around MJD 52950. Unusually, the spin-down rate increased persistently over $800$ days after the glitch, and the average spin-down rate of post-glitch was about $9.6\%$ larger than pre-glitch. Accompanied with the glitch activity, pulse profile became narrower. The pulsar began to switch between two emission modes after the glitch, with pulse width ($W_{\ 50 \rm mean}$) of $8.5(7)^{\circ}$ and $3.7(3)^{\circ}$, respectively. Besides that, the relatively narrow pulse profile gradually became dominant. All of the observations indicate that there should be connection between magnetospheric behavior and glitch activity. We discuss one possibility of magnetosphere fluctuation triggered by glitch event.