A spin-down clock for cool stars from observations of a 2.5-billion-year-old cluster

Abstract: The ages of the most common stars - low-mass (cool) stars like the Sun, and smaller - are difficult to derive because traditional dating methods use stellar properties that either change little as the stars age or are hard to measure. The rotation rates of all cool stars decrease substantially with time as the stars steadily lose their angular momenta. If properly calibrated, rotation therefore can act as a reliable determinant of their ages based on the method of gyrochronology. To calibrate gyrochronology, the relationship between rotation period and age must be determined for cool stars of different masses, which is best accomplished with rotation period measurements for stars in clusters with well-known ages. Hitherto, such measurements have been possible only in clusters with ages of less than about one billion years, and gyrochronology ages for older stars have been inferred from model predictions. Here we report rotation period measurements for 30 cool stars in the 2.5-billion-year-old cluster NGC 6819. The periods reveal a well-defined relationship between rotation period and stellar mass at the cluster age, suggesting that ages with a precision of order 10 per cent can be derived for large numbers of cool Galactic field stars.

• The paper presents precise rotation period measurements for 30 cool stars in NGC 6819, significantly refining gyrochronology models for older stars.
• It employs Lomb-Scargle periodogram analysis on 3.75 years of Kepler data, achieving approximately 10% precision in age determination.
• The study mitigates observational challenges by integrating radial velocity, proper motion, and spectroscopic data to confirm cluster membership.

Analysis of Observed Rotation Periods for 30 Cool Stars in the NGC 6819 Cluster

The paper under review presents a comprehensive analysis of the rotation periods for 30 cool stars in the 2.5-billion-year-old open cluster NGC 6819. By offering these new measurements, the study contributes significantly to the field of stellar gyrochronology, leveraging data from one of the oldest clusters for which such data has been derived. Given the relative paucity of data for older stellar clusters, this work fills an important gap, thereby enabling a refinement of gyrochronology models for stars older than approximately one billion years.

The authors utilize high-precision photometric time-series data obtained from NASA's Kepler mission to determine the rotational periods. By employing techniques such as Lomb-Scargle periodogram analysis on long-cadence Kepler light curves extending over approximately 3.75 years, the study derives precise rotational data. Notably, the stars observed span a (B-V) color index from 0.41 to 0.89 mag, reflecting a range of stellar masses from about 0.85 to 1.4 solar masses.

Significantly, the research confirms a well-defined rotational sequence for NGC 6819 stars, casting light on the P–t–M surface that characterizes rotational period (P) as a function of time (t) and stellar mass (M). This is particularly notable as the pattern observed in NGC 6819 supports earlier theoretical inferences suggesting that cool main-sequence stars older than the Hyades cluster reside on a distinct gyrochronology surface in P–t–M space. These findings have reduced the uncertainties surrounding stellar gyrochronology ages to approximately 10%, contributing to an accurate calibration of gyrochronology at ages beyond one billion years.

The authors also address potential confounding variables in their data, such as contamination from close-proximity stars and the potential influence of tidal interactions with stellar or planetary companions. Radial velocity and proper motion data were integrated to confirm cluster membership, and the selection of non-variable star sequences, together with assessed vsin(i) values from spectroscopic observations, helped validate their rotational measurements.

A crucial aspect of this study is its implication for the modeling of stellar rotational evolution across considerable time spans. By analyzing the NGC 6819 rotational data, which fits existing gyrochronology models with a mean cluster gyro age of 2.49 billion years (with a standard deviation of 0.25 billion years), the study enhances the empirical constraints for the P–t–M relation. This finding aligns well with classical stellar evolution models, affirming the reliability of gyrochronology as a method for age determination.

Ultimately, the paper forwards both theoretical and practical progress within astrophysics. On a theoretical level, it sharpens gyrochronology by extending its applicability to cooler stars in older cluster populations. Practically, it facilitates age determination for cool field stars with a similar level of precision, which could prove invaluable for studying astrophysical phenomena evolving over time.

Future developments may further refine rotational models to increase the precision of ages derived for stars with complex rotational histories or unique characteristics, leveraging larger sets of observational data that might be gathered by new telescopic technologies or subsequent iterations of the Kepler mission's methodologies.

This work, therefore, demarcates a significant advance in our understanding of stellar evolution, offering reliable methods for evaluating the ages of stars and refining our grasp of rotational dynamics over extensive temporal frameworks.