Angular Momentum Transport in Magnetized Stellar Radiative Zones. II. The Solar Spin-down

Abstract

We present a large set of numerical calculations describing the rotational evolution of a solar-type star, in response to the torque exerted on it by a magnetically coupled wind emanating from its surface. We consider a situation where the internal redistribution of angular momentum in the radiative part of the envelope is dominated by magnetic stresses arising from the shearing of a preexisting, large-scale, poloidal magnetic field. By assuming a time-independent poloidal magnetic field, neglecting fluid motions in meridional planes, and restricting our attention to axisymmetric systems, we reduce the spin-down problem to solving the (coupled) ψ-components of the momentum and induction equations. Nevertheless, our computations remain dynamical, in that they take into account both the generation of a toroidal magnetic field by shearing of the preexisting poloidal field, and the back-reaction of the resulting Lorentz force on the differential rotation. It becomes possible to draw, for the first time, a reasonably realistic and quantitative picture of the effects of large-scale internal magnetic fields on the main-sequence rotational evolution of solar-type stars. We perform spin-down calculations for a standard solar model, starting from the ZAMS and extending all the way to the solar age. The wind-induced surface torque is computed using the axisymmetric formulation of Weber & Davis (1967). We consider a number of poloidal magnetic field configurations which differ both in the degree of magnetic coupling between the convective envelope and radiative core and in average strength. The rotational evolution can be divided into three more or less distinct phases: an initial phase of toroidal field buildup in the radiative zone, lasting from a few times 104 to a few times 106 yr; a second period in which oscillations set up in the radiative zone during the first phase are damped; and a third period, lasting from an age of about 107 yr onward, characterized by a state of dynamical balance between the total stresses (magnetic + viscous) at the core-envelope interface and the wind-induced surface torque, leading to a quasistatic internal magnetic and rotational evolution. Our results also demonstrate (1) the existence of classes of large-scale internal magnetic fields that can accommodate rapid spin-down near the ZAMS and yield a weak internal differential rotation by the solar age, (2) the importance of phase mixing in efficiently damping large-scale toroidal oscillations pervading the radiative interior at early times, (3) the near-independence of the present solar surface angular velocity on the strength and geometry (past and present) of any internal large-scale magnetic field pervading the radiative interior, and (4) the greater dependence of the present solar internal differential rotation on the overall morphology (but not on the strength) of the internal magnetic field.