Evaluating the Limits of Rotation Period Recovery through Gyrochronology Criteria
Contamination from nearby sources often compromises stellar rotation periods derived from photometric light curves, particularly in data with large pixel scales such as TESS. This problem is compounded when both the target and contaminant are intrinsically variable, a scenario that challenges deblending algorithms, which often assume constant contaminants. We assess the reliability of rotation period detections using wide binary systems, whose components share a common age and rotational history. By applying gyrochronology constraints, we identify period combinations that yield consistent ages between components, helping to isolate true rotation signals. Simulating blends with degraded Kepler data, our method recovers correct rotation periods with an 88\% success rate for periods $<12$ days, where TESS detections are most reliable. Applying this framework to nearly 300 wide binaries observed by TESS, we find that despite significant contamination, a subset of pairs shows consistent gyrochronological ages. We establish a practical detection threshold for TESS blended observations, finding that periods shorter than $\sim8$ days are reliably recovered, while those longer than $\sim10$ days become significantly more challenging and often remain unresolved. As expected, rotation periods are more often recovered when the highest-amplitude periodogram peak is linked to the brighter star and the second to the dimmer star, although many cases deviate from this pattern, indicating it cannot always be assumed. Our results highlight the limitations of standard deblending methods and demonstrate that astrophysical constraints, such as gyrochronology, provide a valuable tool for extracting reliable rotation periods from complex photometric blends.