Stellar models simulating the disk-locking mechanism and the evolutionary history of the Orion Nebula cluster and NGC 2264

Context. Rotational evolution in young stars is described by pre–main sequence evolutionary tracks including non-gray boundary conditions, rotation, conservation of angular momentum, and simulations of disk-locking. Aims. By assuming that disk-locking is the regulation mechanism for the stellar angular velocity during the early stages of pre–main sequence evolution, we use our rotating models and observational data to constrain disk lifetimes (Tdisk) of a representative sample of low-mass stars in two young clusters, the Orion Nebula cluster (ONC) and NGC 2264, and to better understand their rotational evolution. Methods. The period distributions of the ONC and NGC 2264 are known to be bimodal and to depend on the stellar mass. To follow the rotational evolution of these two clusters’ stars, we generated sets of evolutionary tracks from a fully convective configuration with low central temperatures (before D- and Li-burning). We assumed that the evolution of fast rotators can be represented by models considering conservation of angular momentum during all stages and of moderate rotators by models considering conservation of angular velocity during the first stages of evolution. With these models we estimate a mass and an age for all stars. Results. The resulting mass distribution for the bulk of the cluster population is in the ranges of 0.2−0.4 M⊙ and 0.1−0.6 M⊙ for the ONC and NGC 2264, respectively. For the ONC, we assume that the secondary peak in the period distribution is due to high-mass objects still locked in their disks, with a locking period (Plock) of ~8 days. For NGC 2264 we make two hypotheses: (1) the stars in the secondary peak are still locked with Plock = 5 days, and (2) NGC 2264 is in a later stage in the rotational evolution. Hypothesis 2 implies in a disk-locking scenario with Plock = 8 days, a disk lifetime of 1 Myr and, after that, constant angular momentum evolution. We then simulated the period distribution of NGC 2264 when the mean age of the cluster was 1 Myr. Dichotomy and bimodality appear in the simulated distribution, presenting one peak at 2 days and another one at 5−7 days, indicating that the assumption of Plock = 8 days is plausible. Our hypotheses are compared with observational disk diagnoses available in the literature for the ONC and NGC 2264, such as near-infrared excess, Hα emission, and spectral energy distribution slope in the mid-infrared. Conclusions. Disk-locking models with Plock = 8 days and 0.2 Myr ≤ Tdisk ≤ 3 Myr are consistent with observed periods of moderate rotators of the ONC. For NGC 2264, the more promising explanation for the observed period distribution is an evolution with disk-locking (with Plock near 8 days) during the first 1 Myr, approximately, but after this, the evolution continued with constant angular momentum