Rotation Periods of ZAMS Stars

Studies using direct detection of periods via rotational modulation have been carried out on stars in several young clusters which are near the zero--age main sequence (ZAMS), including the Hyades, the Pleiades and Persei (see Radick 1988, Schaller et al. 1992 and Prosser 1992 respectively). The ages of these clusters are about 700, 70 and 50Myr respectively. Comparison of these data leads to the following conclusions (Soderblom 1996):

1. Rotation in ZAMS clusters has a strong mass dependence. High--mass stars tend to rotate much more quickly than the low--mass stars.
2. The two younger clusters, Persei and the Pleiades, contain ultra--fast rotators (UFRs) with km/s at all masses.
3. The maximum rotation rate is highest in the youngest cluster, and the fraction of UFRs is also highest in this cluster.

When combining these results with those on TTs, problems develop. If one sets the initial rotation periods, masses and radii observed for TTs and then allows them to evolve forward, the resulting distribution of rotation periods doesn't resemble the distribution of rotation periods observed in young clusters. Barnes and Sofia (1996) argue the UFRs cannot be produced if Skumanich--like spin down occurs on the pre--main sequence. They argue that the magnetic field saturates beyond a threshold rotational velocity and has a very strong dipole. This limits the rate at which angular momentum transfer occurs through the magnetic field and causes UFRs to exist in cases of relatively short disk survival. Once stars reach the main sequence, all stars experience a Skumanich--like slowdown due to angular momentum loss via their winds (Endal & Sofia 1981). Recent work (cf. Barry 1988, Walter & Barry 1991) indicate that the spin--down rate is a function of the mass and is proportional to (where A is a constant). The result is that younger stars are expected to spin down more quickly and older stars spin down more slowly than expected with the Skumanich law.

In order to explain the slow down of the UFRs to the rate of the other slower rotators, core--envelope decoupling has been suggested (cf. Li & Collier--Cameron 1993, Strom 1994). In the models, the core decouples from the envelope of a young star. The core is free to spin--up in accordance with , without a noticeable change to the stellar surface rotation. According to such models, in time, angular momentum in transferred out to the envelope. Meanwhile, all stars slow down due to wind losses. This model is tunable, depending on the coupling between the core and the envelope. Stars on their radiative tracks can either speed up or slow down their observed rotational velocities. By moving the decoupling radius for stars of various ages and various masses, the observed distributions can be reproduced. This seems to be a case of too many free parameters, and not enough data. The models can be constrained somewhat by including younger stars into the database. These stars will provide fiducial positions for rotation period as a function of age. The data on the young stars will teach us exactly what the usual rotation rate is as a function of mass and age.