Stellar cycle and evolution of polar spots in an M+WD binary

Stellar activity cycles reveal continuous relaxation and induction of magnetic fields. The activity cycle is typically traced through the observation of cyclic variations in total brightness or Ca H&K emission flux of stars, as well as cyclic variations of orbital periods of binary systems. In this work, we report the identification of a semi-detached binary system (TIC 16320250) consisting of a white dwarf (0.67 $M_{\odot}$) and an active M dwarf (0.56 $M_{\odot}$). The long-term multi-band optical light curves spanning twenty years revealed three repeated patterns, suggestive of a possible activity cycle of about ten years of the M dwarf. Light curve fitting indicates the repeated variation is caused by the evolution, particularly the motion, of polar spots. The significant Ca H&K, H$\alpha$, ultra-violet, and X-ray emissions imply that the M dwarf is one of the most magnetically active stars. We propose that in the era of large time-domain photometric sky surveys (e.g., ASAS-SN, ZTF, LSST, Sitian), long-term light curve modeling can be a valuable tool for tracing and revealing stellar activity cycle, especially for stars in binary systems.