The color-period diagram and stellar rotational evolution - New rotation period measurements in the open cluster M34

Abstract

We present the results of a 5 month photometric time-series survey for stellar rotation periods combined with a 4 year radial-velocity survey for membership and binarity in the 220Myr open cluster M34. We report surface rotation periods for 120 stars, 83 of which are kinematic and photometric late-type cluster members. A comparison to previous work serves to illustrate the importance of high-cadence long baseline photometric observations and membership information. The new M34 periods are less biased against slow rotation and cleaned for non-members. The rotation periods of the cluster members span over more than an order of magnitude from 0.5 days up to 11.5days, and trace two distinct rotational sequences - fast (C) and moderate-to-slow (I) - in the color-period diagram. The sequences represent two different states (fast and slow) in the rotational evolution of the late-type cluster members. We use the color-period diagrams for M34 and for younger and older clusters to estimate 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 suggests a quick transition. We estimate a lower limit on the maximum spin-down rate (dP/dt) during this transition to be 0.06daysMyr-1 and 0.08daysMyr-1 for early and late K dwarfs, respectively. We compare the I sequence rotation periods in M34 and the Hyades for G and K dwarfs and find that K dwarfs spin down slower than the Skumanich √t rate. We determine a gyrochronology age of 240Myr for M34. The gyro-age has a small formal uncertainty of 2% which reflects the tight I sequence in the M34 color-period diagram. We measure the effect of cluster age uncertainties on the gyrochronology age for M34 and find the resulting error on the gyro-age to be consistent with the 15% error estimate for the technique in general. We use the M34 I sequence to redetermine the coefficients in the expression for rotational dependence on color used in gyrochronology. Finally, we propose that stability in the phase, shape, and amplitude of the photometric variability for the 120 rotators over the 5 month duration of our survey is due to spot generation at active stellar longitudes. © 2011. The American Astronomical Society. All rights reserved.