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Description
We have Fourier-analyzed 941 K2 light curves (LCs) of likely members of Praesepe, measuring periods for 86% and increasing the number of rotation periods (P) by nearly a factor of four. The distribution of P versus (V-Ks), a mass proxy, has three different regimes: (V-Ks)<1.3, where the rotation rate rapidly slows as mass decreases; 1.3<(V-Ks)<4.5, where the rotation rate slows more gradually as mass decreases; and (V-Ks)>4.5, where the rotation rate rapidly increases as mass decreases. In this last regime, there is a bimodal distribution of periods, with few between ~2 and ~10 days. We interpret this to mean that once M stars start to slow down, they do so rapidly. The K2 period-color distribution in Praesepe (~790Myr) is much different than that in the Pleiades (~125Myr) for late F, G, K, and early-M stars; the overall distribution moves to longer periods and is better described by two line segments. For mid-M stars, the relationship has a similarly broad scatter and is steeper in Praesepe. The diversity of LCs and of periodogram types is similar in the two clusters; about a quarter of the periodic stars in both clusters have multiple significant periods. Multi- periodic stars dominate among the higher masses, starting at a bluer color in Praesepe ((V-Ks)~1.5) than in the Pleiades ((V-Ks)~2.6). In Praesepe, there are relatively more LCs that have two widely separated periods, {Delta}P>6days. Some of these could be examples of M star binaries where one star has spun down but the other has not.
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