  The open cluster M67 offers the 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, 75d observation window, crowded
field, and typically low-amplitude signals mean determining accurate rotation
periods on the order of 25 - 30d is inherently difficult. Lingering,
non-astrophysical signals with power at >25d 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 35d 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 15% recovery rate for the solar case (i.e. 25d 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.
