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

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Abstract

The ages of the most common stars—low-mass (cool) stars like the Sun, and smaller—are difficult to derive1,2 because traditional dating methods use stellar properties that either change little as the stars age3,4 or are hard to measure5,6,7,8. 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 gyrochronology2,9,10,11. 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 years12,13,14,15,16, and gyrochronology ages for older stars have been inferred from model predictions2,7,11,17. 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.

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Figure 1: The schematic PtM surface for cool stars.
Figure 2: The colour–period diagram for NGC 6819.
Figure 3: Comparison between gyrochronology models and the NGC 6819 CPD.

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Acknowledgements

S.M. acknowledges support through NASA grant NNX09AH18A (The Kepler Cluster Study), NSF grant 1312882 (The Kepler Cluster Study: Planets and Gyrochronology) and the Smithsonian Institution’s Competitive Grants Program for Science in 2012 and 2013. S.A.B. acknowledges support from the German Science Foundation (DFG) during a crucial phase of this work via a Mercator Guest Professorship at the University of Potsdam and the Leibniz Institute for Astrophysics Potsdam, Germany. This paper includes data collected by the Kepler mission. Kepler was competitively selected as the tenth Discovery mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. Some or all of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX13AC07G and by other grants and contracts. Spectroscopic observations of NGC 6819 with the Hectochelle spectrograph were obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona.

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Authors and Affiliations

Authors

Contributions

S.M. is the Principal Investigator for The Kepler Cluster Study and led the planning and execution of the study; the determination and validation of rotation periods from the Kepler data; the membership, binarity and vsin(i) survey in NGC 6819 with the Hectochelle spectrograph on the MMT telescope; and the writing of this paper. S.A.B. is a Co-Investigator on The Kepler Cluster Study and participated in planning the study, evaluated the light curves for periodicity, performed the gyrochronology analysis and age determination for the stars, and collaborated closely with S.M. in writing the paper. I.P. is a Co-Investigator on The Kepler Cluster Study and contributed to the selection of Kepler targets in NGC 6819 with proper-motion membership information and to the analysis of crowding and contamination in the vicinity of target stars from deep, high-spatial-resolution images of this star cluster. R.L.G. is a Co-Investigator on The Kepler Cluster Study and contributed to the selection of Kepler targets in NGC 6819 with analysis of crowding and contamination in deep, high-spatial-resolution images. He carried out analysis of alternative methods for extracting light curves from raw Kepler data. D.W.L. participated in the NGC 6819 radial-velocity membership and binarity surveys, and led the preparation of the Kepler Input Catalog. R.D.M. is the Principal Investigator of the WIYN Open Cluster Study, which contributed radial-velocity measurements to the membership and binary star surveys in NGC 6819.

Corresponding author

Correspondence to Søren Meibom.

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Extended data figures and tables

Extended Data Figure 1 The light curves, phase-folded light curves and periodograms for the stars KIC 5111207, 5023899, 5024227, 5023760, 5024122 and 5113601.

For each star we show a segment of the full Kepler light curve used for determining its rotation period (a), the corresponding phase-folded light curve (b), and the periodogram (power as a function of rotation frequency, c). The KIC identification number44 and the measured rotation period for each star are shown above the light curve segments.

Extended Data Figure 2 The light curves, phase-folded light curves and periodograms for the stars KIC 5112499, 5026583, 4938993, 5111834, 5111908 and 5024856.

See Extended Data Fig. 1 for details.

Extended Data Figure 3 The light curves, phase-folded light curves, and periodograms for the stars KIC 5112507, 5024280, 5023796, 5024008, 5023724 and 5023875.

See Extended Data Fig. 1 for details.

Extended Data Figure 4 The light curves, phase-folded light curves and periodograms for the stars KIC 5112268, 5111939, 5025271, 4937169, 5112871 and 5023666.

See Extended Data Fig. 1 for details.

Extended Data Figure 5 The light curves, phase-folded light curves and periodograms for the stars KIC 5024182, 5023926, 4937149, 4936891, 4937119 and 4937356.

See Extended Data Fig. 1 for details.

Extended Data Figure 6 The NGC 6819 colour–magnitude diagram.

The colour–magnitude diagram for stars identified as common proper-motion members of NGC 681925 and located within 5 arcmin of the cluster centre. The diagonal band tracing a tight relationship between the de-reddened photometric colour index, (B − V)0, and brightness, V, represents the population of cluster members. The locations of the 30 stars with measured rotation periods are marked with larger red circles. They all fall along this band and are thus photometric members of NGC 6819. Stellar masses in solar units are given along the top horizontal axis at the corresponding colours. The light from distant binary companions causes the two rotators near (B − V)0 = 0.5 mag to fall above the cluster sequence.

Extended Data Figure 7 Pixel mask images for NGC 6819 members.

Examples of pixel mask images (PMI) for the accepted star KIC 4938993 (a) and the rejected stars KIC 5023712 (b) and KIC 5287900 (c). Semi-transparent green circles mark the positions of KIC sources. Red dots correspond to the positions of fainter sources from deeper surveys within the Kepler field. The solid blue line traces the optimal aperture (optimizing the signal-to-noise ratio for the target) defined for each target star in each quarter. The shape, size and location of the optimal aperture typically differed for the different quarters of observations.

Extended Data Figure 8 A comparison of rotation periods and projected rotation velocities for stars in NGC 6819.

Projected rotation velocities (vsin(i)) plotted against the measured rotation periods for stars in NGC 6819. For comparison, three solid black curves show the expected relations between rotation period and vsin(i) for stars with respective radii of 0.85, 1.0 and 1.4 solar radii, observed at an inclination angle of their spin axes (i) of 90°. All stars plotted have single-lined spectra. The average rotation velocity resolution in the Hectochelle spectra is 7.38 km s−1. The agreement between the expected and observed vsin(i) values for the measured rotation periods provides additional validation of our rotation period measurements.

Extended Data Figure 9 The gyro age distribution for 21 cool dwarf members of NGC 6819.

The gyrochronology ages for the 21 stars in the NGC 6819 CPD with (B − V)0 colours in the range from 0.55 to 0.9 mag (masses between 1.1 and 0.85 solar masses). The mean and median of the distribution are 2.49 and 2.43 Gyr, respectively. The standard deviation for the 21 gyro ages is 0.25 Gyr, or 10% of the mean gyro age for the cluster. The standard error of the 2.49 Gyr mean is 0.056 Gyr, or 2%.

Extended Data Table 1 Basic parameters and rotation period measurements for 30 members of NGC 6819

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Meibom, S., Barnes, S., Platais, I. et al. A spin-down clock for cool stars from observations of a 2.5-billion-year-old cluster. Nature 517, 589–591 (2015). https://doi.org/10.1038/nature14118

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