Pre-Main Sequence and Main Sequence Rotational Evolution: Constraints on Models Derived from Observations

Abstract

We describe a simple, parameterized model for the redistribution of angular momentum within the interiors of solar-type stars. Among other things, it enables us to treat: (i) the outward flow of angular momentum from the radiative interior in response to rotational deceleration of the overlying convection zone; and (ii) the reapportionment of angular momentum between the core and convective envelope during pre-main sequence evolution. By combining the model with a computation of the rate of angular momentum removal by a magnetically-coupled wind, we can trace the rotational histories of low-mass dwarf stars for a variety of initial conditions and parameter specifications. We present the results of calculations of the rotational evolution of a 1M⊙ star, from an age ≈ few × 106 years up to the age of the present-day sun. We compare these results with what is known from observations about the internal rotation of the sun and the evolution of the surface rotation of sun-like stars. Within the context of the present model, we find best agreement with the constraints imposed by observations of main sequence stars for: (i) a surface magnetic field strength which is only weakly dependent on surface angular velocity f for rapid rotation, becoming linearly-dependent on Ω for Ω ≈ Ω⊙; and (ii) a time scale for angular momentum transfer from the core to the convection zone which is relatively constant throughout the evolution, with magnitude ∼ 107 years. For the adopted description of rotational braking by a magnetized wind, only a small fraction (∼ 10–15%) of the initial angular momentum is lost during pre-main sequence evolution, with most of this loss occurring just prior to arrival on the zero-age main sequence. As a result, Ω increases during most of the process of contraction to the main sequence. The amount of spin-up and some of the details of the subsequent rotational evolution are dependent upon the prescribed core-envelope coupling time.