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 per cent precision per data point for 13 less than or similar to i less than or similar to 17. Candidate cluster members were selected from a V versus V - I colour-magnitude diagram over 14 < V < 24 (0.12 less than or similar to M/M-circle dot less than or similar to 1.0), finding 714 candidates, of which we expect similar to 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 lognormal distribution in dN/d log M. Searching for periodic variable objects in the candidate members gave 105 detections over the mass range 0.25 < M/M-circle dot < 1.0. The distribution of rotation periods for 0.4 < M/M-circle dot < 1.0 was found to peak at similar to 7 d, with a tail of fast rotators down to periods of similar to 0.8 d. For 0.25 < M/M-circle dot < 0.4 we found a peak at short periods, with a lack of slow rotators (e.g. P greater than or similar to 5 d), consistent with the work of other authors 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 similar to a factor of 2 lower than in the Pleiades, consistent with models of angular momentum evolution assuming solid body rotation without needing to invoke core-envelope decoupling.