The evolution of the solar inner rotation by the Eddington-Sweet type circulation under the influence of the solar wind torque

Abstract The evolution of the axisymmetric rotation of the radiative interior of the sun is investigated. The basic equations are derived within the framework of the Eddington-Sweet theory of perturbation. The effect of the molecular weight gradient built up by the proton-proton reaction and the effect of the solar wind torque are taken into account. The initial state of the rotation is assumed to be rigid body rotation and to have an angular velocity about 20 to 65 times larger than the present surface value. The numerical calculations are performed by the two-term approximation of the Legendre expansion. The results show that the Eddington-Sweet circulation brings the angular momentum inwards to partially spin up (not spin down) the deep interior. The convection zone suffers a double extraction of the angular momentum: one from the above inner transport by the Eddington-Sweet circulation and the second from the solar wind torque. Thus, the present decline of the surface angular velocity is faster than that for the case in which only the convection zone is spun down. The time the surface angular velocity takes to decline to the present value is estimated to be on the order of 107 to 108 years. This clearly shows the necessity of some mechanism which brings the angular momentum out from the solar interior.