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

We present the results of a five month photometric time-series survey for stellar rotation over a 40' X 40' field centered on the 150 Myr open cluster M35. We report rotation periods for 441 stars within this field and determine their cluster membership and binarity based on a decade-long radial velocity survey, proper-motion measurements, and multiband photometric observations. We find that 310 of the stars with measured rotation periods are late-type members of M35. The distribution of rotation periods for cluster members span more than 2 orders of magnitude from ~0.1 to 15 days, not constrained by the sampling frequency and the timespan of the survey. With an age between the zero-age main sequence and the Hyades, and with ~6 times more rotation periods than measured in the Pleiades, M35 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 color (mass). The M35 color-period diagram enables us to determine timescales for the transition between the two rotational states, of ~60 Myr and ~140 Myr for G and K dwarfs, respectively. These timescales are inversely related to the mass of the convective envelope, and offer constraints on the rates of internal and external angular momentum transport and of the evolution of stellar dynamos. A comparison to the Hyades, confirm the Skumanich spin-down dependence for G dwarfs on one rotational state, 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 rotational isochrones to determine ages for coeval stellar populations. We use such gyrochronology to determine 'gyro-ages' for M35 from 134 Myr to 161 Myr. We use the M35 data to evaluate new color dependences for the rotational isochrones.