ON THE EVOLUTION OF ROTATIONAL VELOCITY DISTRIBUTIONS FOR SOLAR-TYPE STARS

We investigate how the distribution of rotational velocities for late- type stars of a given mass evolves with age, both before and during re sidence on the main sequence. Starting from an age similar to 10(6) ye ars, an assumed pre-main sequence rotational velocity/period distribut ion is evolved forward in time using the model described by MacGregor and Brenner (1991) to trace the rotational histories of single, consti tuent 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 inte rior to the convective envelope in response to the rotational decelera tion of the stellar surface layers; and (iii), angular momentum redist ribution associated with changes in internal structure during the proc ess of contraction to the main sequence. We ascertain how the evolutio n of a specified, initial rotational velocity/period distribution is a ffected 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 tau(c) character izing the transfer of angular momentum from the core to the envelope; (ii) differences in the details and duration of pre-main sequence stru ctural evolution for stars with masses in the range 0.8 less than or e qual to M/M. less than or equal to 1.0; and (iv), the exchange of ang ular momentum between a star and a surrounding, magnetized accretion d isk during the first few million years of pre-main sequence evolution following the development of a radiative core. The results of this ext ensive parameter study are compared with the distributions derived fro m measurements of rotational velocities of solar-type stars in open cl usters with known ages. Starting from an initial distribution compiled from observations of rotation among T Tauri stars, we find that reaso nable agreement with the distribution evolution inferred from cluster observations is obtained for: (i) a dynamo law in which the strength o f the coronal field increases linearly with surface angular velocity f or rotation rates less than or equal to 20 times the present solar rat e, and becomes saturated for more rapid rotation; (ii) a coupling time scale similar to 10(7) years; (iii) a mix of stellar masses consisting of roughly equal numbers of 0.8 M. and 1.0 M. stars; and (iv), disk r egulation of the surface rotation up to an age similar to 6 x 10(6) ye ars for stars with initial rotation periods longer than 5 days. A numb er of discrepancies remain, however: even with the most favorable choi ce of model parameters, the present calculations fail to produce a suf ficiently large proportion of slow (equatorial velocities less than 10 kms(-1)) rotators on the Zero-Age Main Sequence.