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Super-Orbital Variations in Magnetar Rotation Measure Arising from the Precession of Companion Star: Implications for FRB 20220529

Recent observations of FRB 20220529 reveal significant variation and a partial reversal in its rotation measure (RM), suggesting the presence of a dynamically evolving magnetized environment, which could be caused by the orbital motion of the magnetar within the binary system. Here we develop the binary model by suggesting that the spin and magnetic axis of the companion star could undergo precession around the orbital axis. It is then investigated how the precession period and the inclination of the magnetic axis, as well as a possible disc wind, can influence the evolution behaviors of the RM and dispersion measure (DM) of FRB emission. As the foremost consequence, the RM variation can be significantly altered on timescales longer than the orbital period, producing super-orbital evolution and complex patterns. Applying this model to FRB 20220529, we find that its RM evolution could be reproduced with a precession period of 182 days and an inclination angle of approximately $19^{\circ}$, while the other binary parameters are fixed at their typical values. Meanwhile, the absence of significant variation of the DM argues against the presence of a dense equatorial disc around the companion star, which would be constrained by future long-term observations.