| Summary: | The open cluster M67 offers a unique opportunity to measure rotation periods for solar-age stars across a range of masses, potentially filling a critical gap in the understanding of angular momentum loss in older main sequence stars. The observation of M67 by NASA K2 Campaign 5 provided light curves with high enough precision to make this task possible, albeit challenging, as the pointing instability, 75 day observation window, crowded field, and typically low-amplitude signals mean that determining accurate rotation periods on the order of 25-30 days is inherently difficult. Lingering, non-astrophysical signals with power at ≥25 days found in a set of Campaign 5 A and F stars compounds the problem. To achieve a quantitative understanding of the best-case scenario limits for reliable period detection imposed by these inconveniences, we embarked on a comprehensive set of injection tests, injecting 120,000 sinusoidal signals with periods ranging from 5 to 35 days and amplitudes from 0.05% to 3.0% into real Campaign 5 M67 light curves processed using two different pipelines. We attempted to recover the signals using a normalized version of the Lomb-Scargle periodogram and setting a detection threshold. We find that, while the reliability of detected periods is high, the completeness (sensitivity) drops rapidly with increasing period and decreasing amplitude, maxing at a 15% recovery rate for the solar case (i.e., 25 day period, 0.1% amplitude). This study highlights the need for caution in determining M67 rotation periods from Campaign 5 data, but this can be extended to other clusters observed by K2 (and soon, TESS).
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