Magnetic activities of two contact binaries in quadruple stellar systems

Based on observations from the Transiting Exoplanet Survey Satellite (TESS), we conducted a comprehensive study of two contact binaries, V752 Cen and HT Vir, in 2+2-type hierarchical quadruple stellar systems. TESS continuous light curves (LCs) reveal that [Formula: see text] exhibits random-walk-like or quasi-periodic variations, whereas [Formula: see text], shows small jumps. Using the Wilson-Devinney program, we obtained six sets of photometric solutions to trace the migration and evolution of a cool starspot on the stellar surface. Notably, such spot activity can significantly alter LCs and may even reverse minima depths, as observed around BJD[Formula: see text]2459282 for V752 Cen. From the TESS time-series LCs, we determined 529 eclipse timings (ETs). For HT Vir, the residuals of the primary and secondary minima show a strong anti-correlation, indicating the presence of starspots. Based on all available ETs, we constructed [Formula: see text] curves, which could be described by an upward parabola with the light-time effect (LiTE) induced by a third body. Given the third light of [Formula: see text] for HT Vir, we estimate the mass of the third body to be [Formula: see text]. For V752 Cen, the minimum mass of the third body is [Formula: see text], suggesting it may be a compact star. Finally, we updated the absolute parameters of the two studied binaries, whose components are normal or slightly evolved main-sequence stars.