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

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.Comment: 55 pages, 22 figures, published by Ap

The K2 M67 Study: A Curiously Young Star in an Eclipsing Binary in an Old Open Cluster

We present an analysis of a slightly eccentric ($e=0.05$), partially eclipsing long-period ($P = 69.73$ d) main sequence binary system (WOCS 12009, Sanders 1247) in the benchmark old open cluster M67. Using Kepler K2 and ground-based photometry along with a large set of new and reanalyzed spectra, we derived highly precise masses ($1.111\pm0.015$ and $0.748\pm0.005 M_\odot$) and radii ($1.071\pm0.008\pm0.003$ and $0.713\pm0.019\pm0.026 R_\odot$, with statistical and systematic error estimates) for the stars. The radius of the secondary star is in agreement with theory. The primary, however, is approximately $15\%$ smaller than reasonable isochrones for the cluster predict. Our best explanation is that the primary star was produced from the merger of two stars, as this can also account for the non-detection of photospheric lithium and its higher temperature relative to other cluster main sequence stars at the same $V$ magnitude. To understand the dynamical characteristics (low measured rotational line broadening of the primary star and the low eccentricity of the current binary orbit), we believe that the most probable (but not the only) explanation is the tidal evolution of a close binary within a primordial triple system (possibly after a period of Kozai-Lidov oscillations), leading to merger approximately 1Gyr ago. This star appears to be a future blue straggler that is being revealed as the cluster ages and the most massive main sequence stars die out.Comment: 33 pages, 11 figures, accepted to AJ, photometry files will be available with the electronic journal articl

Understanding angular momentum evolution of solar-age stars with K2 data

Gyrochronology, which describes the empirical relationship among stellar mass, rotation period, and age, is a potentially powerful tool for determining the ages of stars, upon which the understanding of stellar evolutionary models hangs. Well-calibrated with open clusters up to the age of ~2.5 Gyr, predictions from gyrochronology are in conflict with asteroseismic observations of older stars, and the underlying physics are poorly understood. The solar-age, open cluster M67, recently observed by the NASA K2 mission, offers the opportunity to test both gyrochronology and more physically-motivated angular momentum evolution models. Here, we seek to gain insight into the angular momentum evolution of solar-age stars through the analysis of K2 data. Using our own pipeline, we extract and process K2 light curves that encompass the inner and outer portions of M67. We describe various rotation period detection methods, focusing on the Lomb-Scargle periodogram, autocorrelation function (ACF), and Gaussian processes (GPs), before presenting our own preliminary results. Observed scatter between colour and period, combined with disagreement from the first published sets of K2 M67 periods, prompted a comprehensive round of sinusoidal injection tests to probe our absolute detection limits with K2 data using two different light curve preparation pipelines. Finding low sensitivity for 25 d, 0.1% amplitude signals and lingering systematics on the order of 25 d and greater, we use a combination of the Lomb-Scargle, ACF, and GP methods to determine our ‘final’ M67 rotation periods from K2 data. We find agreement between tidal synchronization theory and observed rotation periods for our M67 binaries. While angular momentum evolution models may perform slightly better than gyrochronology, we cannot make any conclusive statements regarding the validity of either due to the inherent scatter and small sample size. Future work at refining detection methods is needed, along with complementary data from upcoming missions such as LSST and PLATO.</p

Understanding angular momentum evolution of solar-age stars with K2 data

Gyrochronology, which describes the empirical relationship among stellar mass, rotation period, and age, is a potentially powerful tool for determining the ages of stars, upon which the understanding of stellar evolutionary models hangs. Well-calibrated with open clusters up to the age of ~2.5 Gyr, predictions from gyrochronology are in conflict with asteroseismic observations of older stars, and the underlying physics are poorly understood. The solar-age, open cluster M67, recently observed by the NASA K2 mission, offers the opportunity to test both gyrochronology and more physically-motivated angular momentum evolution models. Here, we seek to gain insight into the angular momentum evolution of solar-age stars through the analysis of K2 data. Using our own pipeline, we extract and process K2 light curves that encompass the inner and outer portions of M67. We describe various rotation period detection methods, focusing on the Lomb-Scargle periodogram, autocorrelation function (ACF), and Gaussian processes (GPs), before presenting our own preliminary results. Observed scatter between colour and period, combined with disagreement from the first published sets of K2 M67 periods, prompted a comprehensive round of sinusoidal injection tests to probe our absolute detection limits with K2 data using two different light curve preparation pipelines. Finding low sensitivity for 25 d, 0.1% amplitude signals and lingering systematics on the order of 25 d and greater, we use a combination of the Lomb-Scargle, ACF, and GP methods to determine our âfinalâ M67 rotation periods from K2 data. We find agreement between tidal synchronization theory and observed rotation periods for our M67 binaries. While angular momentum evolution models may perform slightly better than gyrochronology, we cannot make any conclusive statements regarding the validity of either due to the inherent scatter and small sample size. Future work at refining detection methods is needed, along with complementary data from upcoming missions such as LSST and PLATO.</p