The Monitor Project: Stellar rotation at 13~Myr: I. A photometric monitoring survey of the young open cluster h~Per

We aim at constraining the angular momentum evolution of low mass stars by measuring their rotation rates when they begin to evolve freely towards the ZAMS, i.e. after the disk accretion phase has stopped. We conducted a multi-site photometric monitoring of the young open cluster h Persei that has an age of ~13 Myr. The observations were done in the I-band using 4 different telescopes and the variability study is sensitive to periods from less than 0.2 day to 20 days. Rotation periods are derived for 586 candidate cluster members over the mass range 0.4<=M/Msun<=1.4. The rotation period distribution indicates a sligthly higher fraction of fast rotators for the lower mass objects, although the lower and upper envelopes of the rotation period distribution, located respectively at ~0.2-0.3d and ~10d, are remarkably flat over the whole mass range. We combine this period distribution with previous results obtained in younger and older clusters to model the angular momentum evolution of low mass stars during the PMS. The h Per cluster provides the first statistically robust estimate of the rotational period distribution of solar-type and lower mass stars at the end of the PMS accretion phase (>10 Myr). The results are consistent with models that assume significant core-envelope decoupling during the angular momentum evolution to the ZAMS.