Rotation Periods for Cool Stars in Open Clusters NGC 6709 and NGC 6940

Open clusters are used to calibrate the relationship between mass, rotation, and age because member stars are nearly homogeneous, having been born about the same time from the same molecular clouds. Rotation rates are expected to decrease with time as stars lose angular momentum through mechanisms such as stellar winds. We selected two open clusters for our study: NGC 6709 which is a young open cluster similar to the Pleiades with an estimated age of 150 Myrs, and NGC 6940 which is an open cluster slightly older than the Hyades with an estimated age of 750 Myrs. These two clusters are observed over multiple months using the robotic observatory STELLA to obtain photometry for the F, G, K, and M stars. The resulting frames are processed using the Daophot II software package to get PSF photometry and then combined to make light curves for each star. Using four time series analysis methods, rotation periods are obtained for the first time for cluster members. The rotation periods of these stars are plotted against their respective Gaia EDR3 colors, a proxy for mass. NGC 6709 shows a sequence of slow rotators with longer rotation periods towards redder stars with a few rapid rotators that have not yet joined this sequence. This distribution is very similar to that of the Pleiades and other similarly-aged open clusters. NGC 6940, as an older cluster, has a similar slow rotator sequence, but this sequence is overall slower than that of NGC 6709, and fewer stars inhabit the rapidly rotating regime, as expected for an older cluster