The Monitor project: Rotation of low-mass stars in the open cluster M34

We report on the results of a V and i -band time-series photometric survey of M34 (NGC 1039) using the Wide Field Camera (WFC) on the Isaac Newton Telescope (INT), achieving better than 1% precision per data point for 13 < ∼ i < ∼ 17. Candidate cluster members were selected from a V vs V − I colour-magnitude diagram over 14 < V < 24 (0 . 12 < ∼ M/ M ⊙ < ∼ 1 . 0), finding 714 candidates, of which we expect ∼ 400 to be real cluster members (taking into account contamination from the field). The mass function was computed, and found to be consistent with a log-normal distribution in dN / dlogM. Searching for periodic variable objects in the candidate members gave 105 detections over the mass range 0 . 25 < M/ M ⊙ < 1 . 0. The distribution of rotation periods for 0 . 4 < M/ M ⊙ < 1 . 0 was found to peak at ∼ 7 days, with a tail of fast rotators down to periods of ∼ 0 . 8 days. For 0 . 25 < M/ M ⊙ < 0 . 4 we found a peak at short periods, with a lack of slow rotators (eg. P > ∼ 5 days), consistent with the work of other authors (eg. Scholz & Eisl¨offel 2004) at very low masses. Our results are interpreted in the context of previous work, finding that we reproduce the same general features in the rotational period distributions. A number of rapid rotators were found with velocities ∼ a factor of two lower than in the Pleiades, consistent with models of angular momentum evolution assuming solid body rotation without needing to invoke core-envelope decoupling.