Gyrochronology is the study of stellar spin down with respect to age. Open clusters
contain mostly homogenous stars and thus are ideal to calibrate the dependence of
rotation rates on stellar mass and age. We select for this study NGC 6709, a young
open cluster (∼ 150 Myr) with at least one red giant member that is similar in age
to the Pleiades. We take a series of observations from May 2015 to June 2018 with
the AIP's STELLar Activity 1.2m telescope (STELLA1) and apply the point spread function
to construct individual time series for 305 cluster members in our field. We search
for periods within the time series utilizing four data analysis techniques: the phase
dispersion minimization method, the string length method, the generalized Lomb-Scargle
method, and the CLEAN method. Of the 305 cluster member stars, periods are recovered
for the photometric light curves of 60 stars. We plot the Gaia colors of these stars
against their periods to obtain a color-period diagram (CPD). The CPD has two main
features: a sequence of slow rotators that fall along a diagonal where period increases
with redder stars, and a less populated clump of rapidly rotating cool stars. The
area between these two regimes is sparsely populated. We compare the results to several
gyrochronology models of stellar spin down by using isochrones. The bifurcation of
rotation periods is explained by the transition of stars between rapid and slow rotation
as they spin down over time. The CPD of NGC 6709 is similar to those of clusters with
ages around 110-160 Myrs, such as the Pleiades and NGC 2516, demonstrating consistency
in stellar rotation, activity, and age across different clusters.
