Rotation of Late-type Stars in Praesepe with K2

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 - K-s), a mass proxy, has three different regimes: (V - K-s) < 1.3, where the rotation rate rapidly slows as mass decreases; 1.3 < (V - K-s) < 4.5, where the rotation rate slows more gradually as mass decreases; and (V - K-s) > 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 similar to 2 and similar to 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 (similar to 790 Myr) is much different than that in the Pleiades (similar to 125 Myr) 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 - K-s) similar to 1.5) than in the Pleiades ((V - K-s) similar to 2.6). In Praesepe, there are relatively more LCs that have two widely separated periods, Delta P > 6 days. Some of these could be examples of M star binaries where one star has spun down but the other has not.