The K2 M67 Study: Establishing the Limits of Stellar Rotation Period Measurements in M67 with K2 Campaign 5 Data

TL;DR

This study assesses the limits of measuring stellar rotation periods in M67 using K2 data, revealing that detection reliability decreases with longer periods and lower amplitudes, especially around 25 days.

Contribution

It provides a comprehensive analysis of the detection limits for stellar rotation periods in M67 with K2 data, using extensive injection tests and two data processing pipelines.

Findings

Detection reliability is high for short periods and larger amplitudes.

Completeness drops significantly for periods around 25 days and amplitudes below 0.1%.

Maximum recovery rate is about 15% for solar-like rotation signals.

Abstract

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.