Stellar Rotation in Young Clusters: The First 4 Million Years

To investigate what happens to angular momentum during the earliest observable phases of stellar evolution, we searched the literature for periods (P), projected rotational velocities (v sin i), and supporting data on K5–M2 stars (corresponding to masses 0.25–1 M_⊙) from the Orion Nebula Cluster and environs, ρ Ophiuchi, TW Hydra, Taurus-Auriga, NGC 2264, Chamaeleon, Lupus, and η Chamaeleonis. We combine these measures of rotation with the stellar R (as determined from L_bol and T_eff) to compare the data with two extreme cases: conservation of stellar angular velocity and conservation of stellar angular momentum. Analysis of the P data set suggests that the frequency distribution of periods among the youngest and oldest stars in the sample is indistinguishable, while the v sin i data set reveals a decrease in mean v sin i as a function of age. Both results suggest that a significant fraction of all pre–main-sequence (PMS) stars must evolve at nearly constant angular velocity during the first ∼3–5 Myr after they begin their evolution down the convective tracks. Hence, the angular momenta of a significant fraction of pre–main-sequence (PMS) stars must be tightly regulated during the first few million years after they first become observable. This result seems surprising at first glance, because observations of young main-sequence stars reveal a population (30%–40%) of rapidly rotating stars that must begin to spin up at ages t ≪ 5 Myr. To determine whether these apparently contradictory results are reconcilable, we use simple models along with our data set to place limits on (1) the fraction of PMS stars that must be regulated, and (2) the complementary fraction that could spin up as a function of time but escape statistical detection given the broad distribution of stellar rotation rates. These models include (1) instantaneous release at the stellar birthline of a given fraction of stars, with the remaining fraction regulated for 10 Myr; (2) all stars regulated initially, with the released fraction varying linearly with time, and timescales for release of half the stars varying from 0.5 to 5 Myr (i.e., all released by 1 to 10 Myr); and (3) a hybrid model that invokes assumptions (1) and (2). In all cases, we find that a modest population (30%–40%) of PMS stars could be released within the first 1 Myr and still produce period distributions statistically consistent with the observed data. This population is large enough to account for the rapid rotators observed among young main-sequence stars of comparable mass. The limits placed by our models on the fraction of regulated and released stars as a function of time are also consistent with the lifetime of accretion disks as inferred from near-IR excesses, and hence with the hypothesis that disk locking accounts for rotation regulation during early PMS phases.