Signature of a magnetar central engine with precession motion in the X-ray emission of GRB 220711B

The $γ$-ray light curve of long-duration GRB 220711B, is characterized by a multi-peaked structure with a duration lasting $\sim$105 seconds. More interestingly, the X-ray afterglow light curve is composed of a plateau emission smoothly connected with a $\sim t^{-2}$ segment overlapping some flares followed by an extremely steep decay. By analysing the light curves of both prompt emission and X-ray afterglow, no high-confidence-level quasi-periodic oscillation (QPO) signals are found in the light curves of the prompt emission (e.g., BAT and GBM), but it is found that a QPO signal at $\sim$ 50 s above 6$σ$ confidence level indeed exist in the X-ray afterglow. Here, we propose that a supra-massive magnetar as the central engine of GRB 220711B with precession motion is a good interpretation of the features of the X-ray emission. The initial plateau emission and followed decay segment, as well as the extremely steep-decay segment, are consistent with the physical process of supra-massive magnetar spin-down and then collapse into black hole. Moreover, the QPO signal in the X-ray emission can be explained as an effect of the precession motion of the magnetar. If this is the case, one can derive various magnetar parameters such as the initial period ($P_{\rm{0}}$) and surface magnetic field strength ($B_{\rm{p}}$) within a pseudo-redshift range of [1.08, 4.27]. By considering beaming corrections with jet opening angle $5^{\circ}$, we find that $P_{\rm{0}}$ and $B_{\rm{p}}$ lie within the range of [1.87, 6.25] ms and [$1.47\times 10^{16}$, $3.09\times 10^{16}$] G, respectively. The parameter of $B_{\rm{p}}$ is slightly larger than that of other typical long-duration GRBs, but $P_{\rm{0}}$ fall in a reasonable range.