1995A&A...294..469K

We investigate how the distribution of rotational velocities for late-type stars of a given mass evolves with age, both before and during residence on the main sequence. Starting from an age ∼10⁶years, an assumed pre-main sequence rotational velocity/period distribution is evolved forward in time using the model described by MacGregor & Brenner (1991ApJ...376..204M) to trace the rotational histories of single, constituent stars. This model treats: (i) stellar angular momentum loss as a result of the torque applied to the convection zone by a magnetically coupled wind; (ii) angular momentum transport from the radiative interior to the convective envelope in response to the rotational deceleration of the stellar surface layers; and (iii), angular momentum redistribution associated with changes in internal structure during the process of contraction to the main sequence. We ascertain how the evolution of a specified, initial rotational velocity/period distribution is affected by such things as: (i) the dependence of the coronal magnetic field strength on rotation rate through a prescribed, phenomenological dynamo relation; (ii) the magnitude of the timescale τ_c characterizing the transfer of angular momentum from the core to the envelope; (ii) differences in the details and duration of pre-main sequence structural evolution for stars with masses in the range 0.8≤M_*/M_☉≤1.0; and (iv), the exchange of angular momentum between a star and a surrounding, magnetized accretion disk during the first few million years of pre-main sequence evolution following the development of a radiative core. The results of this extensive parameter study are compared with the distributions derived from measurements of rotational velocities of solar-type stars in open clusters with known ages. Starting from an initial distribution compiled from observations of rotation among T Tauri stars, we find that reasonable agreement with the distribution evolution inferred from cluster observations is obtained for: (i) a dynamo law in which the strength of the coronal field increases linearly with surface angular velocity for rotation rates ≤20 times the present solar rate, and becomes saturated for more rapid rotation; (ii) a coupling timescale ∼10⁷years; (iii) a mix of stellar masses consisting of roughly equal numbers of 0.8M_☉ and 1.0M_☉ stars; and (iv), disk regulation of the surface rotation up to an age ∼6x10⁶years for stars with initial rotation periods longer than 5days. A number of discrepancies remain, however: even with the most favorable choice of model parameters, the present calculations fail to produce a sufficiently large proportion of slow (equatorial velocities less than 10km/s) rotators on the Zero-Age Main Sequence.