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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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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Forward Modeling of the Kepler Stellar Rotation Period Distribution: Interpreting Periods from Mixed and Biased Stellar Populations
The Astrophysical Journal (2019)