Investigating the rotational evolution of young, low-mass stars using Monte Carlo simulations

Context. Young stars rotate well below break-up velocity, which is thought to result from the magnetic coupling with their accretion disk. Aims. We investigate the rotational evolution of young stars under the disk-locking hypothesis through Monte Carlo simulations. Methods. Our simulations included 280 000 stars, each of which was initially assigned a mass, a rotational period, and a mass accretion rate. The mass accretion rate depends on both mass and time, following power-law indices of 1.4 and -1.5, respectively. A mass-dependent accretion threshold was defined below which a star was considered as diskless, which resulted in a distribution of disk lifetimes that matches observations. Stars were evolved at constant angular spin rate while accreting and at constant angular momentum when they became diskless. Results. Starting with a bimodal distribution of periods for disk and diskless stars, we recovered the bimodal period distribution seen in several young clusters. The short-period peak mostly consists of diskless stars, and the long-period peak is mainly populated by accreting stars. Both distributions, however, present a long tail toward long periods, and a population of slowly rotating diskless stars is observed at all ages. We reproduced the observed correlations between disk fraction and spin rate, as well as between IR excess and rotational period. The period-mass relation we derived from the simulations only shows the same global trend as observed in young clusters when we released the disk-locking assumption for the lowest mass stars. Finally, we find that the time evolution of median specific angular momentum follows a power-law index of -0.65 for accreting stars, as expected from disk locking, and of -0.53 for diskless stars, a shallower slope that results from a wide distribution of disk lifetimes. At the end of the accretion phase, our simulations reproduce the angular momentum distribution of the low-mass members of the 13 Myr h Per cluster. Conclusions. Using observationally documented distributions of disk lifetimes, mass accretion rates, and initial rotation periods, and evolving an initial population from 1 to 12 Myr, we reproduced the main characteristics of pre-main sequence angular momentum evolution, which supports the disk-locking hypothesis.