The Binary-Binary Hierarchical System XY Leo: A Laboratory for Stellar Activity and Concealed Companions

The hierarchical multiple system XY Leo, despite nearly 90 yr of observations, remains enigmatic. It offers a unique testbed for close binary evolution, involving processes such as mass transfer, angular momentum loss, and the von Zeipel--Kozai--Lidov (ZKL) mechanism. Previously identified as a quadruple system, XY Leo shows long-term orbital period modulations. Our new ground-based and Transiting Exoplanet Survey Satellite data suggest that these may stem from either magnetic cycles or the influence of an unseen companion. While the latter remains speculative, both scenarios are discussed within a unified framework. Using all available photometric and spectroscopic data, we derived ultraprecise physical parameters for the contact binary XY Leo A as $M_{\rm A1}=0.629\pm0.009\,M_{\odot}$, $M_{\rm A2}=0.865\pm0.012\,M_{\odot}$, $R_{\rm A1}=0.739\pm0.007\,R_{\odot}$, $R_{\rm A2}=0.855\pm0.008\,R_{\odot}$, $L_{\rm A1}=0.271\pm0.026\,L_{\odot}$, $L_{\rm A2}=0.288\pm0.030\,L_{\odot}$, and orbital separation $a_{\rm A}=2.078\pm0.010\,R_{\odot}$, based on simultaneous solutions of light and radial velocity curves. The detached binary subsystem XY Leo B is confirmed to be on a wide $\sim 20$-year orbit around the contact system. A second $\sim 23$-year modulation is also detected, which may arise from either stellar magnetic activity or an additional unseen companion. After removing both trends, a coherent residual modulation with a characteristic timescale of $14.2 \pm 0.8$~yr remains in the $O$--$C$ diagram, consistent with a magnetic activity cycle of Applegate type. We modeled XY Leo A with the Cambridge STARS (EV/TWIN) code under non-conservative evolution, finding strong agreement between the tracks and observed parameters, highlighting the system's value for testing multiple-star evolution.