Two Periodic Activity Epochs in FRB 20201124A: Coincident with Critical RM Evolution Epochs and Its Implications

Recent observations of the repeating fast radio burst FRB 20201124A by the Five-hundred-meter Aperture Spherical radio Telescope (FAST) revealed a second-scale periodic modulation ($\sim$1.7\,s) in burst activity during two distinct observational windows. We find that these two periodic activity epochs temporally coincide with the transitional states of the source's Faraday rotation measure (RM), and the chance coincidence is only about 0.07$\%$. This correlation is can be understood within the magnetar/Be-star binary system framework. Considering that only the polar cap region can remain stable for such an extended period, we apply a coherent linear periodic evolution model to jointly constrain the initial burst period \( P_0 \) and the period derivative \( \dot{P} \) across both observation windows (MJD 59310 and MJD 59347). We obtain spin parameters consistent with blind search results: an initial spin period $P_0 = 1.7060155$\,s at the reference time and spin period derivative $\dot{P} = 6.1393 \times 10^{-10}$\,s\,s$^{-1}$. We conclude that during these two observational windows, the magnetar was just crossing the disk of the Be star. The disk-magnetar interaction at these two geometric positions may surpress the multi-polar magnetic fields at low latitudes of the magnetar, which enhances the dominance of the polar cap region emissions and makes the periodic activity detectable.