tokens: We thank Pierre Maxted for interesting discussions and John Southworth for help compiling Table 6 . This paper includes data collected by the Kepler / K 2 mission. Funding for the K 2 mission of Kepler is provided by the NASA Science Mission directorate. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST) under support by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Finally, we would like to thank the anonymous referee for their careful reading of the manuscript and helpful suggestions for improvement. Facilities: Kepler ( K2 ), Keck:I, Sloan , CTIO:2MASS, FLWO:2MASS , WISE . Software: astropy (Astropy Collaboration et al. 2013 ), emcee (Foreman-Mackey et al. 2013 ), george (Ambikasaran et al. 2014 ).
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