Quantifying the Limits of TESS Stellar Rotation Measurements with the K2-TESS Overlap

The Transiting Exoplanet Survey Satellite (TESS) has provided stellar rotation periods across much of the sky through high-precision light curves, but the reliability and completeness of these measurements require careful evaluation. We assess the accuracy of TESS-derived rotation periods by leveraging a cross-matched sample of ~23,000 stars observed by both TESS and the K2 mission, treating K2 periods as a benchmark. Using causal pixel models to extract light curves and the Lomb-Scargle (LS) periodogram to identify rotation signals, we quantify the empirical uncertainties, reliability, and completeness of TESS rotation period measurements. We find that uncertainties on TESS-derived rotation periods are typically below 3% for stars with periods < 10 days. Rotation periods are generally reliable out to 10 days, with >80% of measurements matching the K2 benchmark. Completeness and reliability drop dramatically for periods beyond ~12 days due to the 27-day sector limitation. Stricter cuts on TESS magnitude and LS power improve reliability; the highest LS power tested (>0.2) ensures >90% reliability below 10 days but removes over half of potential detections. Stitching consecutive-sector light curves reduces period uncertainties but does not improve overall reliability or completeness due to persistent systematics. Our findings and code provide a framework for interpreting TESS-derived rotation periods and inform the selection of quality cuts to optimize studies of stellar rotation, young associations, and gyrochronology.