We compare the X-ray profiles and fluxes of the Crab pulsar before and after the glitches in 2017 and 2019, using the data collected by the Insight-HXMT, NICER, and Fermi/GBM, to test whether there is any evidence for magnetosphere rearrangement after glitch. For the 2017 glitch, the profiles from Insight-HXMT (27–200 keV) and NICER (0.5–10 keV) remain unchanged within rms 0.47% and 0.28%, respectively, while the pulsed fluxes measured by these two detectors remain stable with 1σ uncertainty of 0.07% and 0.011%. Considering that the persistent offset of the spin-down rate post-glitch is 0.13% and the X-ray luminosity of the Crab pulsar is proportional to E ̇ 1.6 ± 0.3 , we find that the X-ray flux does not increase proportionally to the spin-down power at a significance of about 2.8σ by fitting the flux measurements with a Heaviside function, and thus the additional torque constantly braking the pulsar spin post-glitch is unlikely due to a global magnetosphere variation. For the 2019 glitch, after which a possible soft X-ray polarization variation was detected, the profiles remain unchanged within rms 2.02%, 0.35%, 0.90%, and 0.47% in 10–200, 0.5–10, 3–4.5, and 27–200 keV, respectively, suggesting that the geometry of the X-ray emitting region after the glitch is similar to the pre-glitch one. Therefore the possible polarization variation during the 2019 glitch is unlikely a consequence of the overall magnetosphere changes. The invariance of the pulse profiles is also verified by Kolmogorov–Smirnov tests and that of pulsed fluxes by Z-tests.
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