DEEP MMT TRANSIT SURVEY OF THE OPEN CLUSTER M37. III. STELLAR ROTATION AT 550 Myr

In the course of conducting a deep (14.5 less than or similar to r less than or similar to 23), 20 night survey for transiting planets in the rich similar to 550 Myr old open cluster M37, we have measured the rotation periods of 575 stars, which lie near the cluster main sequence, with masses 0.2 M-circle dot less than or similar to M less than or similar to 1.3 M-circle dot. This is the largest sample of rotation periods for a cluster older than 500 Myr. Using this rich sample we investigate a number of relations between rotation period, color, and the amplitude of photometric variability. Stars with M greater than or similar to 0.8 M-circle dot show a tight correlation between period and mass with heavier stars rotating more rapidly. There is a group of four stars with P > 15 days that fall well above this relation, which, if real, would present a significant challenge to theories of stellar angular momentum evolution. Below 0.8 M-circle dot, the stars continue to follow the period-mass correlation but with a broad tail of rapid rotators that expands to shorter periods with decreasing mass. We combine these results with observations of other open clusters to test the standard theory of lower main-sequence stellar angular momentum evolution. We find that the model reproduces the observations for solar-mass stars, but discrepancies are apparent for stars with 0.6 less than or similar to M less than or similar to 1.0 M-circle dot. We also find that for late K through early M dwarf stars in this cluster, rapid rotators tend to be bluer than slow rotators in B - V but redder than slow rotators in V - I-C. This result supports the hypothesis that the significant discrepancy between the observed and predicted temperatures and radii of low-mass main-sequence stars is due to stellar activity.