Stellar Rotation in M35: Mass-Period Relations, Spin-Down Rates, and Gyrochronology

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Abstract
We present the results of a 5 month photometric time-series survey for stellar rotation on the 150Myr open cluster M35. We report rotation periods for 441 stars and determine their cluster membership and binarity based on a decade-long radial-velocity survey, and proper-motion and photometric observations. We find that 310 of the stars with measured rotation periods are late-type members of M35. Their rotation periods spans more than two orders of magnitude from ~0.1- 15 days, not constrained by the sampling frequency and the time-span of the survey. With an age bridging the gap between the ZAMS and the Hyades, and with ~6 times more rotation periods than measured in the Pleiades, these new data permit detailed studies of early rotational evolution of late-type stars. Nearly 80% of the 310 rotators lie on two distinct sequences in the color-period plane, and define clear relations between stellar rotation period and stellar color (mass). The M35 color-period diagram enables us to determine the timescale for the transition between the two rotational states as a function of stellar mass. These timescales are inversely related to the mass of the convective envelope, and may offer constraints on the rates of internal and external angular momentum transport and on the evolution rates of stellar dynamos. From a comparison to the Hyades, our data confirm the Skumanich (1972) spindown time-dependence for G dwarfs, but suggest that K dwarfs spin down more slowly. The locations of the rotational sequences in the M35 color-period diagram support the use of rotation al isochrones to determine ages for coeval stellar populations. We use such gyrochronology to determine a "gyro-age" of M35 of 134 Myr with a formal uncertainty of 3Myr. The M35 data are also used to evaluate new color dependencies for the rotational isochrones

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