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We present results from a 5-month photometric survey for stellar rotationperiods combined with a 4-year radial-velocity survey for membership andbinarity in the 220Myr open cluster M34. We report surface rotation periods for120 stars, 83 of which are late-type cluster members. A comparison to previouswork serves to illustrate the importance of high cadence long baselinephotometric observations and membership information. The new M34 periods areless biased against slow rotation and cleaned for non-members. The rotationperiods of the cluster members span more than an order of magnitude from 0.5day up to 11.5 days, and trace two distinct rotational sequences - fast (C) andmoderate-to-slow (I) - in the color-period diagram. The sequences represent twodifferent states in the rotational evolution of the late-type cluster members.We use the color-period diagrams for M34 and for younger and older clusters toestimate the timescale for the transition from the C to the I sequence and find~<150Myr, ~150-300Myr, and ~300-600Myr for G, early-mid K, and late K dwarfs,respectively. The small number of stars in the gap between C and I suggest aquick transition. We estimate a lower limit on the maximum spin-down rate(dP/dt) during this transition to be ~0.06 days/Myr and ~0.08 days/Myr forearly and late K dwarfs, respectively. We compare the I sequence rotationperiods in M34 and the Hyades for G and K dwarfs and find that K dwarfs spindown slower than the Skumanich rate. We determine a gyrochronology age of240Myr for M34. We measure the effect of cluster age uncertainties on thegyrochronology age for M34 and find the resulting error to be consistent withthe error estimate for the technique. We use the M34 I sequence to redeterminethe coefficients in the expression for rotational dependence on color used ingyrochronology (abridged).

The Color-Period Diagram and Stellar Rotational Evolution - New Rotation Period Measurements in the Open Cluster M34